STAT 101 - Oneonta



5486400-34290011.22.20190011.22.2019STAT 101Topics: Syllabus, Nature of StatisticsHandouts: Green Sheet #1; Syllabus; Assignment Schedule; Anatomy of Statistics (2): 1) Statistical Alphabet, 2) Statistical RelationshipsOnline: All handouts; PowerPoint for the Nature of StatisticsCourse Assignments: Obtain text (see syllabus). Scan through text for general format, etc. Review: Ch. 1, section 1.1Go online to the Anatomy of Statistics link and look at a couple of these documents.Go online, scan through the SPSS Manual Procedures section to get an idea of the current manual’s format. Items below-2286004127500Next Class: Nature of Statistics – Terminology (cont.)Stat Essentials (What I should know from today): Be able to: 1) define “Data”; 2) define a “Variable”; 2) distinguish between objective (response) and explanatory variables; 3) identify variables to be studied when provided a study scenario; 4) other terms if we get there; and 5) syllabus. Problem 1.1: Nutrition According to a study published in the Journal of the American Dietetic Association:CHICAGO – The intake of added sugars in the United States is excessive, estimated by the US Department of Agriculture in 1999-2002 as 17% of calories a day. Consuming foods with added sugars displaces nutrient-dense foods in the diet. Reducing or limiting intake of added sugars is an important objective in providing overall dietary guidance. In a study of nearly 30,000 Americans published in the August 2009 issue of the Journal of the American Dietetic Association, researchers report that race/ethnicity, family income and educational status are independently associated with intake of added sugars. Groups with low income and education are particularly vulnerable to eating diets with high added sugars. [For Release August 4, 2009; excerpt from ADA webpage 8.26.2009]1. Identify an objective variable for this study. What values could this variable assume?2. Identify three explanatory variables. What values could these variables assume?Problem 1.2: Diet Calcium & Blood PressureA heart researcher is interested in studying the relationship between diets which are high in calcium and blood pressure in adult females. The researcher randomly selects 20 female subjects who have high blood pressure. Ten subjects are randomly assigned to try a diet which is high in calcium. The other ten subjects are assigned to a diet with a standard amount of calcium. After one year the average blood pressures for subjects in both groups will be measured and compared to decide if diets high in calcium decrease the average blood pressure.1. Identify an objective variable for this study and its associated values.2. Identify some potential explanatory variables and their associated values (may not be specifically identified in the paragraph).Problem 1.3: Get Married - Gain WeightResearcher Penny Larson and her associates wanted to determine whether young couples who marry or cohabitate are more likely to gain weight than those who stay single. The researchers followed 8,000 men and women from 1995 through 2002 as they matured from the teens to young adults. When the study began, none of the participants were married or living with a romantic partner. By 2002, 14% of the participants were married and 16% were living with a romantic partner. At the end of the study, married or cohabitating women gained, on average, nine (9) pounds more than single women, and married or cohabitating men gained, on average, six (6) pounds more than single men. [p21sullivan]1. Identify an objective variable for this study and its associated values2. Identify an explanatory variable and its associated values.Problem 1.4: Obesity and Artery CalcificationScientists were interested in learning if abdominal obesity is related to coronary artery calcification (CAC). The scientists studied 2,951 participants in the Coronary Artery Risk Development in Young Adults Study to investigate a possible link. Waist and hip girths were measured in 1985-86, 1995-96 (year 10) and in 2000-01 (waist girth only). CAC measurements were taken in 2001-02. The results of the study indicated that abdominal obesity measured by waist girth is associated with early atherosclerosis as measured by the presence of CAC in participants. [p21sullivan]1. Identify an objective variable for this study and its 2. Identify an explanatory variable and its associated values.STAT 101 5638800-36576021.24.190021.24.19TOPICS: Nature of Statistics Terms and RelationshipsDOCUMENTS: HANDOUTS: Green #2; Yellow worksheet #1& 2: 1) Top Films and 2) Twenty-Five Q’s classification AVAILABLE ONLINE: All handouts listed above; Extra Credit #1(available online)ASSIGNMENT:Readings: Ch. 1: sections 1.1-1.2; 1.3 (p. 20-24; sampling); Problems: p. 6 # 1-14, 21,24, 25-29; p. 13 # 1-12, 15, 16, 19–22, 29Finish Worksheets #1 - Top Films and #2 - Twenty-Five QuestionsExtra Credit #1 – available online Items below-2286004127500NEXT CLASS: Nature of Statistics: Sampling, etc.DUE: Extra Credit (EX#1; optional)Stat Essentials (taken from today): Be able to: 1) define terms and relationships as presented on the sheet Anatomy of the Basics: Statistical Terms and Relationships; 2) identify variables and their characteristicsProblem 2.1:FREE SHIPPING on orders $39+*Code: SHIP39 An 8x12, 20 page Shutterfly photo book costs $29.00. How much would it cost given the above discount?Problem 2.2: A heart researcher is interested in studying the relationship between diets which are high in calcium and blood pressure in adult females. The researcher randomly selects 20 female subjects who have high blood pressure. Ten subjects are randomly assigned to try a diet which is high in calcium. The other ten subjects are assigned to a diet with a standard amount of calcium. After one year the average blood pressures for subjects in both groups will be measured and compared to decide if diets high in calcium decrease the average blood pressure.1) Identify the population. 2) What characteristic (variable) of the population is being measured? 3) Identify the sample. 4) Is the purpose of this data collection to perform descriptive or inferential statistics? [P15#1H&M]5) Could blood pressure be used as an explanatory variable in this situation? Problem 2.3:Heroin Use: The National Center for Drug Abuse is conducting a study to determine if heroin usage among teenagers has changed. Historically, about 1.3 percent of teenagers between the ages of 15 and 19 have used heroin one or more times. In a recent survey of 1,824 teenagers, 37 indicated they had used heroin one or more times.1) Identify the population. 2) Identify a variable of interest.3) Identify a sample.4) Is the purpose of this data collection descriptive or inferential?Problem 2.4:Cell Phone Fraud: Lambert and Pinheiro (2006) described a study in which researchers try to identify characteristics of cell phone calls that suggest the phone is being used fraudulently. For each cell phone call, the researchers recorded information on its direction (incoming or outgoing), location (local or roaming), duration, time of day, day of week, and whether the call took place on a weekday or weekend. [WSed3p6]1) Identify the observational units in this study. 2) Identify the qualitative variables and their characteristics. 3) Identify the quantitative variables and their characteristics. 4) Would call duration be a good explanatory variable? Why/why not? Problem 2.5:Student Characteristics: A Case represents all of the information collected from one source, such as a student.Student #1 is a male who does not smoke, who lives in an urban area, and who would prefer to win an Olympic gold medal over an Academy Award or Nobel Prize. He indicates that he exercises 10 hours a week, watches television one hour per week, and has a GPA of 3.33. A resting pulse rate of 58 beats per minute, the oldest of three children and a desire to become a fireman represent other characteristics of this student.Identify the variables for which data were obtained and classify them as qualitative (categorical)/quantitative, discrete/continuous, and provide a measurement level for each variable.If similar information were obtained from 49 other students, which variables might most likely be used as explanatory variables?Problem 2.6:Iceland: According to World Bank data, 90% of Icelanders have access to the Internet. In order to determine this value, what were the units from which this figure was obtained? What was the variable of interest (objective variable) and what were the values of this variable? Identify the variable’s characteristics (Qual/Quant etc.) (L5p.7)If one were to look at the number of people worldwide with access to the Internet, we could record the proportion within each country. In doing so, what would be the population units? What was the variable of interest (objective variable) and what were the values of this variable? Identify the variable’s characteristics (Qual/Quant etc.)STAT 101 5524500-8382031.29.190031.29.19TOPICS: Sampling; Combinations (?)DOCUMENTS: HANDOUTS: Green #3; Yellow #3: Sampling AVAILABLE ONLINE: Green #3; Yellow #3: Sampling; PowerPoint placed online (3): 1) Sampling; 2) Experimental Design; 3) Combinations & PermutationsASSIGNMENTS:Text Readings: Ch. 1: pp. 20-22; Text Problems: p. 6 #15-20, 22, 25-27, 35-38; p.13 #17, 18, 23-25, 30 Items below NEXT CLASS: TOPICS: Combinations etc. (?); Qualitative Data; QUIZ #1 DUE: nothingStat Essentials (taken from today): Be able to: 1) identify sampling approaches; 2) understand relationships among basic statistical terms; 3) distinguish between combinations & permutations. Problem 3.1: The grade for this course is based upon 400 points. These points are converted to a 100-point base to result in a final course grade.How many of the 400 points represent one point of the final grade?Extra credit points are added to those you have accrued throughout the course via exams, etc. If you complete ten extra credit exercises, and receive full credit for them all (i.e. 10 points), by how many points will your final grade increase? Over the course of the semester Elijah elects to not submit three, 10-point class assignments. By how many points would his final grade decrease as a result of not having submitted these three assignments?Problem 3.2: Burglaries: ADT Security Systems advertised that “when you go on vacation, burglars go to work.” Their ad stated that “according to FBI statistics, over 26% of home burglaries take place between Memorial Day and Labor Day.” What is misleading about this statement? (Triola7ed,p15#6)38804851016000Problem 3.3: Election: Review the cartoon to the right. Assume that there are 100 boys and 100 girls. Demonstrate using these 200 students how this student’s conclusion is either correct or incorrect. Present your answer using both numerical computations and sufficient discussion to support your findings. Problem 3.4: Variables: Identify the explanatory and objective variables in the following pairs of variables.Lung capacity and number of years smoking cigarettesBlood alcohol content and the number of alcoholic drinks consumedYear and world record time in a marathonProblem 3.5: O-Tiger price hike: For many years Oneonta had a single-A farm team of the NY Yankees, which was followed by a farm team of the Detroit Tigers. When the Tigers arrived, the prices for seating changed. The following comes from an editorial in the local newspaper about the rise in ticket prices for the local single-A professional baseball team. “General admission season passes for adults will be $155, up from $70, in 2009, while six-seat boxes will go up 500 percent, from $300 to $1,500.” (source: The Daily Star, In Our Opinion column for Feb. 7 & 8, 2009, p D3; this team has since left town) The $85 increase in the single seat price represents how much in terms of a percentage increase?Demonstrate using a numerical analysis whether or not the cost of a six-seat box increased by 500%. Problem 3.6: Seat Belts: Suppose that there are 300 students taking statistics and that they are asked if they always use seat belts.If 27% of the students indicate that they do not always use seat belts, how many students is this?Suppose that in different course 20% of the students do not use seat belts and that the 20% represents 43 students. How many students are in this class?Problem 3.7: SPSS: Data File: Environmental_Sustainability_sp2013.savFinding the data file: Go to my web page > Stat 101: Intro > Data Files > open the file noted above How to obtain Selected Tables and Charts:Frequency Table: Analyze > Descriptive Statistics > Frequency > move variable to right cell > Ok.Bar Chart: Graphs > Legacy Dialog > Bar> Define (leave as is) > move variable to Category Axis cell > OKREFERENCE: SPSS Manual available onlineMake a frequency table of the variable, e1, which represents opinions of whether or not the earth is reaching the population limit it can support. Place your name in the table by including a footnote. [Note1: Footnote: double-click on the table, select Insert from the top menu> footnote.] [Note2: when making a table or chart, if you cannot see the variable name, here e1, drag the left edge of the dialog box to make it larger.] Place this table into the Word document. Using SPSS, make a frequency bar chart of the variable e1 and place it into the document. Moving Tables and Charts into a Word Document:Open a Word document.In SPSS right click on the table/chart to copy. Select the COPY AS option. From the dialog box that opens, select EMF (enhanced metafile format).Move to the Word document and select Paste Special > Picture (enhanced metafile). [Note: Picture (jpeg) and Bitmap options also seem to work.]To reduce the size of the table/chart, click on it, move the cursor to one of the corners, and drag towards the center.To move the table/chart to any location, double click on it. From the top menu select the “Wrap Text” item and then “tight.” [also found on the Page Layout Menu > Wrap Text]Analysis of the statistical output:Below the table and chart, type a paragraph discussing the table that contains 1) an introductory statement; 2) a minimum of two descriptive statements ; and 3) a concluding statement. When discussing the contents of a table/chart/graph remember to use the statistics rather than just words such as “more” and “majority.” Incorporate statistics into your written presentation.4781550041.31.19 no class0041.31.19 no classSTAT 101TOPICS: Sampling, Combinations & Permutations, Qualitative DataDOCUMENTSHANDOUTS: Green #4-5; Yellow #4; CA#1 (online only)AVAILABLE ONLINE: Green #4; Yellow #4; CA#1, Combinations ppt.; Qualitative ppt.; Related Anatomy Sheets (5): 1) Anatomy of a Systematic Random Sample; 2) Qualitative Frequency Table; 3) Pie Chart; 4) Pareto Chart; 5) Bar ChartHWK:Text Readings: Ch. 2 – pp. 56-57 (pie & pareto charts); Anatomy of Statistics – Bar, Pie, Pareto ChartsText Problems: p. 23 #1-3, 7-10, 19-26 Additional problems available on Yellow #3 (Sampling) & #4 (Combinations)5657851168400060255151079500Review Writing Descriptive Statements (located below)Class Assignment #1 (CA#1) – due Tuesday [NOTE: SPSS instructions follow those on Green #3.]-36576015684500Items below Next Class: TOPICS: Qualitative Data; DUE: CA#1Stat Essentials (taken from today): Be able to: Combinations etc.:1) determine the number of samples via combinations; 2) calculating permutations, tree diagrams and the multiplication rule for independent events; Qualitative Data: 1) basics of qualitative data analysis (maybe).-36576014922500COMBINATIONS & PERMUTATIONS on the TI Calculator: Math > Prob > select P or C, input the n and r values > enter; Factorials: enter the number, then go to Math > Prob > !-33337513970000Writing Descriptive Statements:Descriptive statements merely report data presented in a table, a graph/chart, or a statistic, such as the mean. To write a paragraph about a table: 1) introduce the table; 2) provide sentences describing some aspect of the data; and 3) write a summary sentence. 379285514605000Example using the table to the right.[1) Introduction=>] The table to the right presents residents’ ratings of life in the village. [2) Descriptives=>] Approximately 78% of surveyed residents rated life in the village positively (good to excellent). In contrast, 77 of 347 residents (22.2%) rated life in the village as poor to fair. One hundred Eighty-three residents (52.7%) rated the quality of life as “good.”[3) Conclusion=>] In general, it would appear that most residents (77.8%) are satisfied with the quality of life in the village.-36195015240000NOTES: The Rating of Quality table is a SPSS generated table. 1) Use the VALID PERCENT column for percentages. DO NOT use the “Percent” column as it includes missing data. 2) If you use words such as most, more than, fewer, approximately, etc., you MUST include supporting statistical evidence. Example: “Most residents rated life in the village as good.” How much is “most,” 30%, 80%? In contrast, “Most residents (52.7%) rated life in the village as good,” provides the reader with context for the descriptive statement.3) If you include numbers representing counts, also include the associated percentage value (e.g. “Eight respondents (15%) liked the movie.”). It is much easier for a reader to understand 15% than to have to figure out what 8 of 53 represents (15%).4) If you start a sentence with a number, as done above in the third descriptive statement, write it out (e.g. NOT “7 respondents liked …,” but rather “Seven respondents liked …” Additionally, the numbers one (1) through ten (10) are generally written out within sentences; others may be displayed numerically.3368675-63500Problem 4.1: Write a paragraph containing: a sentence introducing the table; two sentences that contain descriptive statements resulting from the table’s content; and a conclusion you can draw from these data. Problem 4.2: Identify the variables and their characteristics:1: The number of doctors who wash their hands between patient visits.2: The majors of randomly selected students at a university.3: The average weight of mature German Shepherds.4: The category which best describes how frequently a person eats chocolate: Frequently, Occasionally, Seldom, Never.5: The temperature this morning at 7:00 a.m.6: The diameter of major league baseballs.7: The average horsepower of ten randomly selected 1.6L MINI Cooper engines.Data Source* VariableQual/QuantDiscrete/ContNom/Ord/Int/Ratio1:_______________________________________________________2:_______________________________________________________3:_______________________________________________________4:_______________________________________________________5:_______________________________________________________6:______________________________________________________7:______________________________________________________*NOTE: Data Source is the population or sample unit from which you obtain the data, not the variable information (data) collected.Problem 4.3: The Tax Man Cometh: The Internal Revenue Service wants to sample 1000 tax returns that were submitted last year to determine the percentage of returns that had a refund. Identify a sampling method that would be appropriate in this situation.Problem 4.4: Prescription Drug Program: The director of a hospital pharmacy chooses at random 100 people age 60 or older from each of three surrounding counties to ask their opinion of a new prescription drug program. Identify the type of sampling used.Problem 4.5: Combinations & PermutationsIce Cream: Thirty-one ice cream flavors > three scoops (different flavors) & a banana = one banana split. A) If the order of the flavors did not matter, how many different combinations of ice cream flavors could be made into a banana split? B) How many different ways could a banana split be made if order matters?30099008636100Permutation CalculationCombination Calculation528510563552.5.190052.5.19STAT 101TOPICS: Combinations; Qualitative DataDOCUMENTSHANDOUTS: Green Sheet #5; Yellow #5 AVAILABLE ONLINE: Green #5; Yellow #5; PowerPoints: Qualitative Data, Contingency TablesASSIGNMENTS:Text Readings - Ch. 2 – pp. 56-57 (pie & pareto charts)Text Problems – if we get here: p. 62 #23, 24 (make bar chart instead of pie), 25, 26. EX#2 (optional)Items below.FORMULAS: Multiplication Rule for Independent Events: [read as: event 1* event 2 * etc.]Permutations: Combinations: -2286004127500Next Class: TOPICS: Qualitative Data; Contingency Tables; Quantitative Data Analysis (?); DUE: EX#2Stat Essentials (taken from today): Be able to: Qualitative Data - 1) build qualitative tables; 2) build qualitative charts: pie, bar, pareto; Statistical Software: 1) accessing and obtaining tables and selected tables in SPSS or Minitab (Dr. Wang’s students); Contingency Tables – 1) build and interpret (if we get here).Problem 5.1: Combinations & PermutationsCoca Cola Directors: There are 11 members on the board of directors for the Coca Cola Company. A) If they must elect a chairperson, first vice president, second vice president; and secretary, how many different slates of four candidates are possible? B) If they must form a four-member ethics committee, how many different committees are possible?30086308318500Permutation CalculationCombination CalculationProblem 5.2:5073650669163000In 2005 a television advertisement for Allstate Auto Insurance noted that last year (2004) 1.3 million people switched to Allstate. What is missing here?Problem 5.3:Permutations & Combinations: You have ten paintings to hang, but only space to hang three. A) How many different ways could these paintings be hung if order matters? B) If order didn’t matter, how many different groups of three paintings could occur? 35433008699500Problem 5.4:Village Life: Identify the variable characteristics below.Variable: Qual or Quant: Measurement Level: Write a brief paragraph regarding the information in this table.(See how to write a paragraph on sheet #4.)Problem 5.5:Cell Phones:Variable: Cell Phone Satisfaction Characteristics are: Categorical/Quant Discrete/Continuous/Neither N/O/I/RValues: 1 = Fair; 2 = Good; 3 = Very Good; 4 = ExcellentData (n=31): 1,2, 3, 3, 3, 2, 2, 3, 3, 4, 3, 1, 3, 1, 3, 3, 3, 2, 2, 4, 3, 3, 3, 2, 2, 4, 4, 3, 3, 3, 3Task 1: Build a qualitative frequency table of the variable Cell Phone. Include a table title, the variable values, frequencies, relative frequencies, cumulative frequencies, and cumulative relative frequencies.Task 2: Build a Bar Chart of the variable Anxiety Level.Task 3: Build a Pie Chart of the variable Anxiety Level.Task 4: Build a Pareto Chart of the variable Anxiety Level.Task5: Write a paragraph that introduces the tables & charts, two sentences that describe information contained within the frequency table, and a summary statement.5257800-22860062.7.190062.7.19STAT 101TOPICS: Qualitative Data (practice); Contingency tablesDOCUMENTSHANDOUTS: Green Sheet #6; Yellow #6; Contingency Tables Reference; CA#2AVAILABLE ONLINE: Green #6; Yellow #6; CA#2; Contingency Table and Quantitative PowerPoints; Anatomy Sheets (5): Contingency tables; Quantitative Frequency Table; Histogram; Dot Plot; Stem-and-Leaf.HWK:Text Readings - Ch. 2 sections 2.1 – 2.2; p. 551 – contingency tablesText Problems: p. 61-64 - # 24, 26, 33, 35, 37, 38. Yellow #6 problems not used in classCA#2Items below-2286004127500Next Class: TOPICS: Quantitative Data: Tables & Charts; DUE: CA#2Stat Essentials (taken from today): Be able to: QUALITATIVE: 1) calculate relative frequency, cumulative frequency, and cumulative relative frequency for response values; 2) build appropriate tables and charts; CONTINGENCY TABLES: 1) build tables; 2) interpret them. Problem 6.1:Contingency Tables – Random Acts of Kindness: On day two of this course I asked members of three classes to respond to the following three questions.If you could, would you tell someone the time if you were asked?A woman in front of you stumbles and drops her groceries. What would you do?A stranger walks up to you and asks to borrow your cell phone so that she can notify a friend where to meet her. Would you loan the phone? Contingency tables can be used to break the data into sub-groups, thereby providing more information about who, in this case, would perform a random act of kindness. Create a contingency table for each of these three questions by sex and include column percentages. Time by Sex Groceries by Sex The Data:37805624635500Phone by SexConsider: Which is the column variable and the row variable and why? What is the size of each table?What happens to cases where one or both variables are not available?Once built, do you see a trend within each table data? Do you see a trend across the three tables? 33451801079500Problem 6.2:Contingency Table – Purple Car People: During a past semester there were 39 purple cars registered on campus. Really?! Who owned these cars and what types of purple cars are various registrants driving? Contingency tables can be used to break the data into sub-groups, thereby providing more information about who, in this case, owns purple cars.Create a contingency table that crosses vehicle Type with Status. Which variable should be the column variable and which the row variable? Consider:Which is the column variable and why? What is the size of this table?Once built, do you see a trend within the data? 5189220-16827572.12.190072.12.19STAT 101TOPICS: Quantitative Data Tables, Charts & GraphsDOCUMENTSHANDOUTS: Green #7; Yellow #7 (Quantitative Data) AVAILABLE ONLINE: Green #7; Yellow #7; PowerPoint (2): Quantitative Data; Frequency Polygons & Ogives; Anatomy Sheets (4): Quantitative Frequency Table; Histogram, Dot Plot, Stem-and-Leaf-2286001397000; HWK:Text Read: Ch. 2 sections 2.1, 2.2.Text Problems: p. 47 #2 – 5, 7, 8, 11, 19, 21, 25, 31 (#31: freq. table AND freq. histogram)Items below.-2286004127500Next Class: TOPICS: Quantitative Data – Charts (cont.)Stat Essentials (taken from today): Be able to: 1) build a frequency table appropriate for the presentation of quantitative data; 2) identify frequency table components – classes, boundaries, etc.; 3) build charts/graphs appropriate to quantitative data – histogram, dot plot, stem-and-leaf, frequency polygon, ogive (won’t get to all today).Problem 7.1: 304800021336000Contingency Tables: Using the table below, find the requested percentages or counts. The data present three cities in which houses were sold and during which month the houses sold. What is the size of this contingency table? ____ by ____Among houses sold in Arlington, what percent were sold in June and July?During August _____% of the houses were sold in Fort Worth.Among all houses _____% were sold in Dallas during September.Looking at the right marginal totals column what does the 131 value represent? T or F: Thirty percent of the houses sold in June were sold in Dallas.T or F: Thirty-two percent of the houses were sold in Fort Worth.T or F: Of the houses sold in July, approximately 25% were sold in Dallas.Problem 7.2: Obtaining statistical output and providing analysisIdeal Weight: Twenty five students reported their ideal weights (in most cases, not their current weight). Weights (lb): 110115123130105119130125120115120120120110120150110130120118120135130135110Create a frequency table containing five classesWrite a paragraph containing an introduction and a minimum of two descriptive statements.Identify:Midpoint of the third class: ___________Boundaries of the first class; ____________Class limits of the second class: ___________Width of the classes: ____________Based upon your table make the following charts/graphs (NOTE: do only those demonstrated today)Histogram Dot plSTAT 1015524500-36576082.14.190082.14.19TOPICS: Quantitative Tables & Charts (cont.)DOCUMENTS:HANDOUTS: Green #8AVAILABLE ONLINE: Green #8; PowerPoints: Distribution Shapes; Sigma; Quantitative Data – Freq. Polygon, Ogive, Line Chart ppt. ANATOMY REFERENCE SHEETS: various charts for quantitative dataHWK:Text Reading: Ch. 2, review sections 2.1-2.2Text Problems: p. 47 #13, 15, 19, 29, 37, using #32, only make a dot plot, no table; using #35, only make a stem-and-leaf plot (no table)CA#3Items below-2286004127500Next Class: TOPICS: Measures of Center (cont.?); distribution shapes; ???SIGMA); DUE: CA#3Stat Essentials (as with prior class): Be able to: 1) build a frequency table appropriate for the presentation of quantitative data; 2) identify frequency table components – classes, boundaries, etc.; 3) build charts/graphs appropriate to quantitative data – histogram, dot plot, stem-and-leaf, frequency polygon, ogive.36106102349500Problem 8.1: Nutrition Bars: (NOTE: Assume Lower Class Limits are shown)How many values are in the data set? How many classes are there? What is the width of a class? How many milligrams of sodium are in the nutrition bar with the highest value? Explain how a relative frequency histogram would differ from the displayed chart. (Hint: Think about how frequency and relative frequency bar charts differ?)Problem 8.2: Contingency Tables: Using the contingency table, 32861252159000find the requested percentages or counts. The data present the opinions of students regarding ecological disaster possibilities based upon their geographic origin. What is the size of this contingency table? ____ by ____Among students from urban areas, what percent strongly agreed?For Unsure respondents, _____% were from Rural areas.Among all respondents, _____% were from Urban Clusters.Looking at the right marginal totals column what does the 30 value represent? Respondents who were from Urban areas and Mildly Disagree with the statement represent what percent of all respondents?T or F: Sixty percent of the respondents were from a Rural area and indicated a Mildly Agree response.T or F: Approximately 17% of respondents were from Urban areas.T or F: Of the respondents selecting Strongly Agree, approximately 33% were from Rural areas.Problem 8.3: Retirement Ages: (Larson & Farber p. 51 #39)Using the following data, build both a single stem and a double stem, stem-and-leaf.Ages:70 54 55 71 57 58 63 65 60 66 57 62 63 60 63 60 66 60 67 69 69 52 61 73Problem 8.4: Retirement Ages: Using the data from problem 8.3, build a frequency table containing five classes. [NOTE: Without a stated starting point, make sure that the minimum value fits into the first class and the maximum value is within the fifth class. If the latter does not occur, either shift the starting point of the first class, while maintaining class width, or increase the size of the class width.]Problem 8.5: Balance: Eyes closed average of two trials (seconds): Right foot: _____Left foot: _____One of the leading health concerns for people over 60 is falling. Balance in walking and standing is dependent on many factors. ()As people grow older, they may have difficulty with their balance. Roughly 9 percent of adults who are 65 and older report having problems with balance. Having good balance means being able to control and maintain your body's position, whether you are moving or remaining still. An intact sense of balance helps you: walk without staggering; get up from a chair without falling; climb stairs without tripping. Balance disorders are one reason older people fall. According to the Centers for Disease Control and Prevention, more than one-third of adults ages 65 years and older fall each year. Among older adults, falls are the leading cause of injury deaths. ()Aging and balance-good news, bad news Running & FitNews, ?April, 2002 ?Here's the bad news. Along with the visible signs of aging, and the obvious declines in the cardiovascular, respiratory, and orthopedic systems, your body is slowly assembling a collection of deficits that significantly reduce your ability to maintain balance. A decrease in balance ability, if nothing else, can increase your risk of acute running injuries such as sprains and falls.Balance is a matter of collecting information from the environment on where your body is in space and how its position is changing, and then responding with adjustments by your musculoskeletal system. Age-related changes occur in the sensory, motor, cognitive, and musculoskeletal systems, all affecting your ability to perceive and process the necessary environmental cues, and to respond quickly and efficiently to the information. Visual acuity, depth perception, contrast sensitivity, and peripheral vision decline with age and these changes reduce or alter the environmental data your brain uses to maintain balance. Meanwhile, your sensitivity to tactile messages, such as vibration and sensory input from the soles of your feet, is also declining, causing you to rely more on your decreased visual abilities. At the same time, the tiny hair cells within the vestibular system are becoming less sensitive to head motion, diminishing the response of the ocular reflex that stabilizes your eyes. These balance deficits a re probably the main reason you will almost never see individuals beyond 60 or so, riding a roller coaster for fun.There is good news, however. First of all, runners and other athletic individuals probably suffer these declines more slowly than their sedentary contemporaries. Even better, there is still more you can do to slow declines in balance ability. To test your balance, try standing on one leg with your arms folded over the raised leg, knee tucked toward your chest, for 30 seconds. You should be able to do this without dropping the raised leg or hopping around. Next, if you felt reasonably stable on one leg, try 30 seconds with your eyes closed. Now try standing on both feet, with one foot directly in front of the other, heel touching toes. Repeat with your eyes closed. If nothing else, you will learn just how important visual cues are in maintaining balance. Exercises that challenge the multiple systems your body uses for balance, such as the two tests above, can slow age-related declines and even improve balance significantly, whatever your starting point.One of the very best things you can do to improve and maintain balance is to use free weights for strength training. Lifting free weights requires attention to posture and form, while core-stabilizing muscles continuously adjust to the motion of the weights. Using a balance ball instead of a bench while lifting free weights, or standing on an unstable surface such as a balance board, further stimulates and challenges your balance.Include balance training in your fitness plan along with the training of the cardiovascular, musculoskeletal, and respiratory systems you get from running. It's one of the best things you can do to slow the aging process. For information on more balance exercises, go to . (Biomechanics, 2001, Vol. 8, No. 11, pp. 79-86); COPYRIGHT 2002 American Running & Fitness Association; COPYRIGHT 2003 Gale Group. Source: 5356860-9906092.19.190092.19.19STAT 101: TOPICS: Distribution Shapes; Time Series Charts; Σ (Sigma); Measures of Center DOCUMENTS:HANDOUTS: Green #9; Yellow #9AVAILABLE ONLINE: Green #9; Yellow #9; EX#3; PowerPoints for: 1) Sigma, 2) Measures of Center; 3) Distributions, 4) Time Series Charts (in with Freq. Polygon & Ogive); Anatomy sheets: SigmaASSIGNMENTS:Text Readings: Ch. 2, sections 2.3, 2.4 Text Problems: p. 48 #21, 23; p. 60 #17 (single stem), 18 (double stem), 29, 32, 34 (part c & d only; will do scatter plots when we get to correlation)EX#3 available Items belowNEXT CLASS: Measures of Center (cont.), Variation, and Position (?) DUE: EX#3504444060515500Stat Essentials (taken from today): Be able to: DISTRIBUTIONS: 1) identify distribution shapes and characteristics; TIME SERIES: 1) create time series chars (line charts) given two variables; SIGMA: 1) understand what the symbol ? (Sigma) means; 2) successfully demonstrate the application of ????MEASURES OF CENTER 1) calculate an arithmetic mean, median, mode; 2) identify when you would use each of these measures.Problem 9.1:An introductory statistics class had three exams, for which the grade distribution of each exam is presented to the right. For each exam describe the distribution’s shape and comment on the exam’s difficulty. 504698011620500[Consider the x-axis point C1 to be the exam’s mean grade.]Distribution ShapeDifficulty of Exam (easy, average, hard)Exam #1:__________________________________50444409144000Exam #2: __________________________________Exam #3: __________________________________Problem 9.2:SIGMA: Given the following data for X and Y, determine the values of Sxx and Syy.XY204 3810102688104288723Problem 9.3:SIGMA: Given the following data for X and Y, determine the values of r. [Note: same data as in problem 9.2.]XY204 3810102688104288723 Problem 9.4Time Series: Create a time series chart of the Murder Rates in New York City5203825-166370102.21.1900102.21.19STAT 101TOPICS: Measures of Center & VariationDOCUMENTS:HANDOUTS: Green sheet #10; Yellow #10; EXAM #1 PART B (located online; supporting materials > Exams (Current Semester) AVAILABLE ONLINE: Green #10; Yellow #10; EXAM #1 PART B (located online; supporting materials > Exams (Current Semester); PowerPoint: Measures of Center, Measures of Variation, Measures of Position.ASSIGNMENTS:Text Review: Ch. 2 section 2.3-2.4; read 2.5Text Problems: p. 77 # 55, 56 [NOTE: INSTRUCTIONS FOR THESE TWO PROBLEMS ARE ON P. 76], 57; p. 90 #1-5, 15-18, 25, 29EXAM #1 PART B Items belowFORMULAS (For Samples):Mean VarianceStandard DeviationDefinition formula): 46328314503700Computational formula): above Median: 1) middle score if odd number of values; 2) mid-point between two middle scores if even number of valuesMode: most frequent value (multiple modes may exist); represents the center of qualitative dataMidrange: minimum+ maximum2NEXT CLASS: TOPIC: Exam #1A DUE: EXAM #1 PART BStat Essentials (taken from today): MEASURES OF CENTER: Be able to: 1) calculate an arithmetic mean, median, mode; 2) identify when you would use each of these measures; MEASURES OF VARIATON: Be able to:1) explain what a standard deviation represents; 2) obtain a standard deviation using either formula (definition or computational); 3) interpret what the standard deviation represents in a given situation; 4) Empirical Rule;.5) Chebychev’s Theorem.Problem 10.1:Blood Pressure: Given the following sample of systolic blood pressures, determine their mean, median, mode, and midrange; using the COMPUTATIONAL FORMULAS, determine the variance and standard deviation for this variable.Systolic Pressures:1201458613311512415398144132Problem 10.2 CRICKETS: THE DATA: Temperature vs. Cricket Chirps: Crickets make a chirping noise by sliding their wings over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (Fahrenheit) and the number of chips per second for the striped ground cricket.X: Temperature (Fo): 69.4 69.7 71.6 75.2 76.3 79.6 80.6 80.6 82.0 82.6 83.3 83.5 84.3 88.6 93.3Y: Chirps/second: 15.4 14.7 16.0 15.5 14.4 15.0 17.1 16.0 17.1 17.2 16.2 17.0 18.4 20.0 19.8 Determine the mean, median, mode, and midrange for both of these variables. 4985385-26670112.26.1900112.26.19STAT 101TOPICS: EXAM #1DOCUMENTS:HANDOUTS: Green #11AVAILABLE ONLINE: Green #11ASSIGNMENTS:TAKE A BREAK AFTER YOU READ THIS (could be on the next quiz)-44132511112500NEXT CLASS: TOPIC: Measures of Variation & Position (probably) DUE: nothing Stat Essentials (taken from today): To see what we knowPortion sizes increase in 'Last Supper' paintings (An application of statistics)By Nanci Hellmich, USA TODAY (3/23/2010)234696011112500If your food portions seem to have grown larger over the years, you have some blessed company.Two researchers analyzed the food and plate sizes in 52 of the most famous paintings of The Last Supper and found that the portion sizes in the paintings have increased dramatically over the past millennium, from years 1000 to 2000.2057400656590ABOVE: "The Last Supper" painting by Duccio, 1308-11. Note the size of the food and drink on the table compared to the size of the heads of Jesus and his disciples.BELOW: "The Last Supper" painting by Tiziano Vecellio Titian.00ABOVE: "The Last Supper" painting by Duccio, 1308-11. Note the size of the food and drink on the table compared to the size of the heads of Jesus and his disciples.BELOW: "The Last Supper" painting by Tiziano Vecellio Titian.Using a computer program, they compared the size of loaves of bread, main dishes and plates to the size of the heads of the disciples and Jesus in the artwork, including Leonardo da Vinci's famous depiction of the event.422719540640000Findings published in April's International Journal of Obesity: Over that 1,000-year period, the main course size increased by 69%, plate size 66% and loaves of bread 23%. The biggest increases in size came after 1500.The researchers used paintings of this event "because it is the most famous supper in history," which artists have been painting for centuries, so the paintings provide information about plate and entree sizes over time, says Brian Wansink, director of the Cornell (University) Food and Brand Lab in Ithaca, N.Y. One possible reason for the increase: Food may have become more available and less expensive, he says.He did the research with his brother, Craig, a professor of religious studies at Virginia Wesleyan College in Norfolk, and a Presbyterian minister.The three Gospels (Matthew, Mark and Luke), which include descriptions of The Last Supper, mention only bread and wine, but many of the paintings have other foods, such as fish, lamb, pork and even eel, says Craig Wansink.The use of fish in the meals is symbolic because it's an image that is used to represent Christianity, he says. Among the reasons for the symbolism: A number of the disciples were fishermen, and Jesus told them "to be fishers of men," he says. Plus, he says, Jesus performed several miracles with fishes and loaves.As Easter approaches, he says, people may want to study the paintings because they illustrate one of the "most important moments in Christianity4832985-3810122.28.1900122.28.19STAT 101: NEXT CLASS IS ON MARCH 19TOPICS: Measures of Variation; Measures of Position (?)DOCUMENTS:HANDOUTS: Green #12AVAILABLE ONLINE: Green #12, PowerPoint: Measures of Position ASSIGNMENT:Text Review: Ch. 2 section 2.4-2.5Yellow #10, as needed Mid-Term Application Assignment-61722010414000Items below FORMULAS (For Samples): Mean, Median, Mode, Midrange, Variance, Standard Deviation on prior pageFive-Number-Summary: Minimum – Q1 – Q2 – Q3 - MaximumChebychev’s Theorem: 1- 1/k2 where k ≥2; Used with any shape distributionEmpirical Rule: Used with normally distribution dataz-score: Pearson’s -60071026924000NEXT CLASS: TOPIC: Measures of Position DUE: Mid-Term Application AssignmentStat Essentials (taken from today): Measures of Variation: Be able to:1) explain what a standard deviation represents; 2) obtain a standard deviation using computational formula; 3) interpret what the standard deviation represents in a given situation; 4) Empirical Rule; Measures of Position: 1) obtain the five-number-summary; 2) interquartile range; 3) build a box plot; 4) determine variability measures: skew (Pearson’s I), Coefficient of Variability, z-score. Problem 12.1:Blood Pressure: Given the following sample of systolic blood pressures, determine their variance, standard deviation -54102018605500using the computational formula.Systolic Pressures:1201458613311512415398144132NOTE: Calculations for the mean, median, mode are on prior green sheet (Problem 10.1).CRICKETS: THE DATA: Temperature vs. Cricket Chirps: Crickets make a chirping noise by sliding their wings over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (Fahrenheit) and the number of chips per second for the striped ground cricket.X: Temperature (Fo): 69.4 69.7 71.6 75.2 76.3 79.6 80.6 80.6 82.0 82.6 83.3 83.5 84.3 88.6 93.3Y: Chirps/second: 15.4 14.7 16.0 15.5 14.4 15.0 17.1 16.0 17.1 17.2 16.2 17.0 18.4 20.0 19.8 -55372019812000Given: ?x???????????????????????x????????????????????????y????????????????????y???????????????????????xy???????????NOTE: Calculations for the mean, median, mode for both of these variables are on prior green sheet (Problem 10.2). Problem 12.2: Using the computational formula, determine the standard deviations for these two variables. Problem 12.3 (z-score): A temperature of 93.3o is how many standard deviations away from the mean? Sixteen chirps per second is how many standard deviations away from the mean? (z-score questions)4871720-166370133.19.1900133.19.19STAT 101TOPICS: Measures of Position; Box plots; z-score; Pearson’s I, Coefficient of Variability (CVAR)DOCUMENTS:HANDOUTS: Green #13; Yellow #13AVAILABLE ONLINE: Green #13; Yellow #13; PowerPoints: Measures of Position, Correlation, RegressionHWK:Text Readings: Ch. 9,sections 9.1, 9.2; Ch. 2 scatter plot p. 58 Text Problems: p. 107 #7 – 14, 21, 26, 31, 35, 61.Items belowFORMULAS: Mean, median, quartiles, variance, standard deviation on prior sheetsz-score: Pearson’s NEXT CLASS: Correlation & Regression; Quiz #3Stat Essentials (taken from today): Be able to: 1) obtain the five-number-summary; 2) build a box plot; 3) determine variability measures: skew (Pearson’s I), Coefficient of Variability, z-score. If we get there: 1) describe general steps leading to the se of regression; 2) make a scatter plot; 3) calculate the Pearson Product Moment Correlation Coefficient, r.CRICKETS: THE DATA: Temperature vs. Cricket Chirps: Crickets make a chirping noise by sliding their wings over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (Fahrenheit) and the number of chips per second for the striped ground cricket.X: Temperature (Fo): 69.4 69.7 71.6 75.2 76.3 79.6 80.6 80.6 82.0 82.6 83.3 83.5 84.3 88.6 93.3Y: Chirps/second: 15.4 14.7 16.0 15.5 14.4 15.0 17.1 16.0 17.1 17.2 16.2 17.0 18.4 20.0 19.8 Given: ?x???????????????????????x????????????????????????y????????????????????y???????????????????????xy???????????REFER TO Green #12 FOR YOUR ANSWERS TO THE FOLLOWING:Determine the mean, median, mode for both of these variables.Using the computational formula, determine the standard deviations for these two variables. Problem 13.1: SkewDetermine, using Pearson’s I, whether or not the variables are skewed. Temperature I: _____Chirps I: _____Yes No (circle one): Given the value of “I,” we would consider this variable approximately normally distributed. Temperature: Yes NoChirps: Yes NoProblem 13.2: z-scoreFor the variable’s maximum value, determine how many standard deviations it is away from the mean. Temperature z = _____Chirps z: _____Problem 13.3: VariabilityDetermine the variability of the variable.Temperature CVAR = _____Chirps CVAR: _____As a result of comparing variability via CVAR, it appears that ______________ has greater variability than ___________.Problem 13.4: Box plotsCreate a modified box plot for each variable. Although you may not need these values, calculate the IQR, upper limit, and lower limit.TemperatureMin: ____ Q1: ____ Q2: ____ Q3: ____ Temperature Box Plot Here (use line as the x-axis)270256082550 ___________________________________________00 ___________________________________________MAX: ____ IQR: ____ L. Limit: ____ U. Limit: ____ Adj. Pt. (if any): ____ChirpsMin: ____ Q1: ____ Q2: ____ Q3: ____ Chirps Box Plot Here (use line as the x-axis)270256082550 ___________________________________________00 ___________________________________________MAX: ____ IQR: ____ L. Limit: ____ U. Limit: ____ Adj. Pt. (if any): ____5257800-274320143.21.1900143.21.19STAT 101NOTE: THIS PAGE IS CA#4TOPICS: Correlation & Regression DOCUMENTS:HANDOUTS: Green #14 (this is CA#4); Yellow #14, Pearson Correlation Coefficient tableAVAILABLE ONLINE: Green #14; Yellow #14; Correlation ppt. & Regression ppt.TABLE: Pearson Correlation Coefficient table HWK:Text Readings (review): Ch. 9, sections 9.1, 9.2; Ch. 2 p. 58 (scatter plot)Text Problems: p. 495 #1-4, 9-12, 15-21, 23523303510160NOTE: Substitute the study’s variables in place of “variable X” and “variable Y.”00NOTE: Substitute the study’s variables in place of “variable X” and “variable Y.”CA#4 (15 pts.); provided below FORMULAS:330551176084NOTE: Rho = 0 indicates there is no linear correlation.Rho ≠ 0 indicates that there is a linear correlation.00NOTE: Rho = 0 indicates there is no linear correlation.Rho ≠ 0 indicates that there is a linear correlation.Hypotheses: Null Hypothesis (H0) vs. Alternative Hypothesis (Ha) for correlations:48190156604000565277057150051663602413000Statistically:In Words:H0: ()H0: There is no linear relationship between variable X and variable Y.Ha: ()Ha: There is a linear relationship between variable X and variable Y.46692765526005466945552600 EXAMPLE (using the variables Height & Weight): H0: H0: There is no linear relationship between HEIGHT and WEIGHT. Ha: Ha: There is a linear relationship between HEIGHT and WEIGHT. Correlation:Regression: [where b1 = slope and b0 = y-intercept] or NEXT CLASS: TOPICS: Correlation & Regression DUE: CA#4Stat Essentials (taken from today): 1) Be able to: 1) identify the steps leading to correlation and regression; 2) conduct a correlation by hand and via SPSS; 3) Scatter Plot – building and interpreting; 4) Read the Pearson’s Correlation Coefficient Table of Critical Values; 5) Basics of Regression.Problem 14.1 (CA#4):Woodpeckers: Forest managers are increasingly concerned about the damage done to animal populations when forests are clear-cut. Woodpeckers are a valuable forest asset, both because they provide nest and roost holes for other animals and birds and because they prey on many forest insect pests. The article “Artificial Trees as a Cavity Substrate for Woodpeckers,” (Journal of Wildlife Management [1983]) reported on a study of how woodpeckers behaved when provided with polystyrene cylinders as an alternative roost and nest cavity substrate. Noted below are selected values of X = ambient temperature (Co) and Y = cavity depth (in centimeters). [Devore & Peck p. 558]Observation: 1 2 3 4 5 6 7 8 9 10 11 12X: Temperature (Co): -6 -3 -2 1 6 10 11 19 21 23 25 26Y: Hole Depth (cm): 21.1 26.0 18.0 19.2 16.9 18.1 16.8 11.8 11.0 12.1 14.8 10.5-56197514478000Given: n = 12? x = 131?y = 196.3? x2 = 2939? y2 = 3445.25? xy = 1622.3NAME: _________________________CA#4[1] What is being studied? Relationship between ____________________________________[1] Does it make sense to study a relationship between these two variables? _____ Why? ________________________________________________________________________[2] State in words the null and alternative correlation hypotheses to be tested. H0: ___________________________________________________________Ha: ___________________________________________________________[5] Make a scatter plot of these variables.[5] If the scatter plot indicates a relationship between these two variables. Calculate the correlation for the two variables.r = _________[1] Determine if the correlation is statistically significant (circle ONE): not sig. ? = .05 ? = .01(Use: Critical Values for the Pearson’s Correlation Coefficient Table; text page A26)Resulting from the statistical significance determination, the following options occur:If yes, go on to regression. If no, regression should not be attempted and best estimate becomes the mean of the Y variable, .518160038100153.26.1900153.26.19STAT 101TOPICS: Correlation & RegressionDOCUMENTS:HANDOUTS: Green #15AVAILABLE ONLINE: Green #15; Normal Distribution ppt.ASSIGNMENT:Text Readings: Ch. 9 section 9.3; Ch. 5, sections 5.1, 5.2Text Problems: p. 505 #7-12, 17, 19Extra Credit #4 (NOTE: date changed to 3.26 out; 2.28 due)Items below.FORMULAS:Correlation & Regression formulas on prior sheetCoefficient of Determination, r2, = Correlation Coefficient, r, squared (r2) OR = 39052518605500NEXT CLASS: TOPICS: Regression (cont?); Normal Distribution DUE: EC#4-80010037528500Stat Essentials (taken from today): Review from prior classes 1) Steps leading to correlation and regression; 2) building and interpreting: scatter plot; hypotheses; correlation, statistical sig. of r; Today: 3) Regression – developing the regression equation; 4) terminology related to correlation & regression.41948101460500Problem 15.1:Given the following data set obtain: 1) in words identify what the null and alternative hypotheses state for this set of data; 2) a correlation coefficient; 3) the significance level of the correlation; 4) the coefficient of determination; 5) the regression equation for the line of best fit; 6) Add the regression line to the scatter plot to right (approximate location); and 7) calculate values for Yogi and Booboo. You may do this problem by manually calculating the values on the back of this sheet or using SPSS. Lengths & Weights of Male Bears Length (in.):53.0 67.5 72.0 72.0 73.5 68.5 73.0 37.0Weight (lbs.):80 344 416 348 262 360 332 34In words state the null and alternative hypotheses for these two variables.H0: ________________________________________________Ha: ________________________________________________r = ____Sig. level of r??? = _____r2 = _____ %Regression Equation for these variables: ______________________Given the regression equation you identified estimate the weight of the following two bears:514359271000Yogi who is 76.0 inches long. Booboo (aka Bobo) who is 43 inches long. Estimated weights: Yogi: ________________________________________________Booboo: ______________________________________________50292000163.28.1900163.28.19STAT 101TOPICS: Corr. & Reg. (?); Normal Distribution; Standard Normal Table DOCUMENTS:HANDOUTS: Green #16; Yellow #16; Standard Normal Table; Practice Sheets; CA#4AVAILABLE ONLINE: Green #16; Yellow #16; Normal Distribution and Distribution of Sample Means PowerPoints; Anatomy (2): Normal Distribution, Standard NormalASSIGNMENT:Text Readings: –Ch. 5, sections 5.1 – 5.3; Text Problems: – (sect., page, problems); p. 506 #18, 30 (note: just determine the regression equation (calories = X), no plot or correlation); p. 112 #62Items below: Do 16.1 & 16.2 [do 16.3-16.6 if we get do the practice sheet]FORMULAS:-4292606985000 Probability Rules: 1) 2) -68897519177000NEXT CLASS: TOPIC: Normal Distribution, Dist. Of Sample Means; DUE CA#7; Quiz #4Statistics Essentials: Know: 1) the characteristics of a standard normal distribution; 2) how to identify a probability distribution; 3) find an area associated with a z-score (use the standard normal table); 4) find a z-score associated with an area (use the standard normal table Problem 16.1: Identify the area associatedProblem 16.2: Identify the z-score associatedwith the following z-scores.with the following areas.1) z = -1.54: area =2) z = .50: area = 1) area = .0207: z = 2) area = .5000: z = 3) z = 2.33: area =4) z = -1.645: area = 3) area = .9500: z = 4) area = .9900: z = Draw the area under the standard normal curve and determine the probability noted.Problem 16.3: P(z 1.62)Problem 16.4: P(-.42 z or z .42)0565150032004008128000Problem 16.5: P(1.00 z 2.50)Problem 16.6: P(-.26 z 0.00)38100143510003176905-11563350051517550174.2.1900174.2.19STAT 101TOPICS: Non-Standard Normal DistributionsDOCUMENTS:HANDOUTS:; Green #17; Yellow #17; CA#5AVAILABLE ONLINE: Green #17; Yellow #17; CA#5; Dist. Of Sample Means ppt.; Normal Dist. Ppt.HWK:Text Readings: Ch. 5, section 5.4 Text Problems: p. 262 #1-4, 33-35; Prior Topics: p. 505 #19; p. 110 #39, 44Problems from Yellow #16 & 17 – selected ones we do not get to in classCA#5Items belowFORMULAS: Dist. Sample Means: ; Pop: NEXT CLASS: TOPICS: Normal Distribution (cont. ?); Confidence Intervals (?) DUE: CA#5Statistics Essentials: Know: 1) application of standard normal to non-standard normal situations; and, if we get there: 2) the characteristics of the distribution of sample means; 3) the Central Limit Theorem.Problem 17.1: Driven to distraction: It seems almost silly to say: Keep your eyes on the road. But with cars now more than ever resembling mobile offices, massive entertainment centers, telephone booths and lunch counters – well, the road is sometimes the last thing we’re looking at. It’s much more interesting to jabber away on the cell phone or toy with your iPod – but those distractions can cut your reaction time in half. And with most accidents occurring within a few seconds, you need all the time you can get. So hang up, find a radio station you like and keep looking forward. (Source: MetLife yourlife, Summer 2007; italics added)So what do you know? Assume it takes you 2 seconds to react and apply the brakes when driving and paying attention to the road. How long will it take you to react while being distracted by food, phone, etc?Problem 17.2: Marriage Patterns: Are more people living together before getting married? The results of a recent survey indicated that 48% of respondents indicated that they were in an unwed relationship and that forty percent of these couples marry within three years. If there were 1200 respondents to the survey, how many of the respondents would marry within three years? 46863001841500Problem 17.3: Education and self-employment: According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean if 13.6 and a standard deviation of 3.0.If one self-employed person was randomly selected, what would be the probability that he/she would have an education level less than 11 years? Problem 17.4: 46710602222500Pregnancy Duration: The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Wanda has been pregnant for a really, really long time. So long in fact that only one-half of a percent of women have been pregnant longer. For how many days has Wanda been pregnant?51517550184.4.1900184.4.19STAT 101TOPICS: Non-Standard Normal Dist.; Dist. of Sample Means; Central Limit TheoremDOCUMENTS:HANDOUTS: Green #18AVAILABLE ONLINE: Green #18; Dist. Of Sample Means ppt.; Confidence Intervals Ppt.HWK:Text Readings: Ch. 6, section 6.1-6.3 Text Problems: p. 274 #1-8, 13, 17; Prior Topics: p. 505 #21; p. 112 #57 [do box plot for “You” data only]Problems from Yellow #16 & #17 – try some problems we did not get to in class; KEYS are onlineItems belowFORMULAS: Dist. Sample Means: ; Pop: NEXT CLASS: Confidence IntervalsStatistics Essentials: Know: 1) application of standard normal to non-standard normal situations; 2) the characteristics of the distribution of sample means; 3) the Central Limit Theorem; 4) application to non-standard normal where n > 1.46634408826500Problem 18.1 (NOTE: continuation of 17.3)Education and self-employment: According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean if 13.6 and a standard deviation of 3.0.Find the mean and standard error of the sampling distribution of the mean for a random sample of size 100.466344010350500If a sample of 100 self-employed individuals is selected, find the probability that their mean education level is less than 11.0 years.Problem 18.2: 58407305822950046488359188450049974506534150062249057664450045485053873500Normal Distribution: PINE TREES: A buyer for the You-Build-It Lumber Company must decide whether or not to buy logging rights on a piece of land containing 15,000 mature pine trees. The heights of mature pine trees are normally distributed and the owner reports that the trees have a mean height of 36 feet and a standard deviation of 4 feet. The buyer will purchase the logging rights if less than 1,000 of the trees are estimated to be shorter than 30 feet tall. Based upon this information, what is the buyer’s decision? A) Draw a picture of this problem.B) How many trees are estimated to be shorter than 30 feet tall? ______C) Explain your answer (i.e. show how you came to your recommendation).D) According to the stipulations cited above, is this a BUY ______ or a DO NOT BUY _______ situation?Problem 18.3Box plot: The table to the right contains the amount of fat per serving in grams of 12 Kelloggs “Children’s” cereals. Construct a box plot of these data.Min: _____ Q1: _____ Q2: _____ Q3: _____ Max: _____ IQR: _____ L. Limit: _____ U. Limit: _____left1619250039624006604000152400151320500Place Box Plot Here:Problem 18.4-34290017081500Correlation & Regression:5351145-3175194.9.1900194.9.19STAT 101TOPICS: Confidence Intervals DOCUMENTS:HANDOUTS: Green #19; Yellow #19; CA#6AVAILABLE ONLINE: Green #19; Yellow #19; CA#6; EX#5; Anatomy Sheets for Confidence Intervals; Confidence Intervals pptRELEVANT ANATOMY SHEETS (4): Z???, Confidence Intervals for Small Samples, Large Samples, & ProportionsASSIGNMENTS:Text Readings: – Ch. 6, sections 6.1 – 6.3CA#6EX#5 (optional)Item(s) below.FORMULAS: Confidence Intervals & sample sizes [NOTE: Probabilities are on Orange #19]102870071691500 NEXT CLASS: TOPIC: Confidence Intervals; DUE: CA#6, EX#5421830545402500Statistics Essentials for Confidence Intervals: Know: 1) what a confidence interval represents and how to calculate one for specific conditions; 2) what a margin of error is and how to obtain it; 3) the table above; 4) obtaining Z??? critical values.Problem 19.1 Pregnancy Duration: The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the mean and standard error of the sampling distribution of the mean for a random sample 10 pregnancies.42468801270000A sample of 10 pregnant women is selected. Find the probability that their mean pregnancy is greater than 283 days.Problem 19.2 Critical Value of za/2: Calculate the za/2 critical value associated with the following Confidence Levels.92%: za/2 = _______96%: za/2 = ______90%: za/2 = _______98%: za/2 = _______43129203302000Problem 19.3Balance-1: Data were collected on the length of time subjects could stand on one foot with eyes closed? Using the data provided in the accompanying table for a random sample of 30 time measures (from N = 94), build 95% confidence intervals about the observed means for left foot up and right foot up.Problem 19.4Balance-2: Using the data from the prior problem, obtain a 90% confidence interval for the left foot up data. Problem 19.5Balance-3: Examine the Left Foot 90% and 95% confidence intervals from the prior problems. What happened to confidence and precision when going from a 90% C.I. to a 95% C.I? Explain why this happens?44297602540000Problem 19.6Balance-4: The N = 94 statistics table to the right presents the mean, ?, and standard deviation, ?, for the studied population. Review the means and determine if they fall within the 95% confidence intervals generated in the previous problems for the samples of size n = 30. Can samples be used to estimate population parameters? What would be some advantages of using samples to estimate population parameters?5295900-274320204.11.1900204.11.19STAT 101TOPICS: Confidence Intervals for Small Samples & Proportions; C.I. sample sizesDOCUMENTS:HANDOUTS: Green #20; Yellow #20AVAILABLE ONLINE: Green #20; Yellow #20; Hypothesis Testing ppt.ASSIGNMENT:Text LARSON: Ch. 7, section 7.1 – 7.3-69776716085000Yellow #20: problems #5, 6, 14, 18Items below and Green problems 19.3-19.6FORMULAS: On prior sheets (Confidence intervals on sheet #19).NEXT CLASS: TOPICS: Confidence Intervals (cont. ?); Hypothesis Testing (at least started maybe?) Statistics Essentials for Confidence Intervals (proportions): Know: 1) how to identify a confidence interval for small samples & proportions; 2) Calculating the intervals; 3) characteristics of the t distribution.Problem 20.1 (Correlation)Problem 20.2 (Confidence Interval)Health Clubs: A random sample of 60 female members of health clubs in Los Angles showed that they spend on average 4 hours per week doing physical exercise with a standard deviation of .75 hours. Find a 95% confidence interval for the population mean ??Problem 20.3: (Normal Distribution)Tall Clubs International: Tall Clubs International is a social organization for tall people. It has a requirement that men must be at least 74 inches tall, and women must be at least 70 inches tall. Man’s heights are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches. Women’s heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. A) What percent of men meet the requirement?B) What percent of women meet the requirement?C) Are the height requirements for men and women fair? Why or why not?5417820-274320214.16.1900214.16.19STAT 101TOPICS: Hypothesis Testing (One Sample)DOCUMENTS:HANDOUTS: Green #21; Yellow #21; CA#7 AVAILABLE ONLINE: Green #21; Yellow #21; CA#7; Hypothesis Testing ppt; REVIEW SHEETS #1-536893507556500ASSIGNMENT:Text LARSON: Ch. 7, section 7.1 – 7.3Text Problems: p. 367 #1-11, 13, 17, 18, 21-23, 25, 26CA#7Items below FORMULAS: Hypothesis TestingSteps in testing a hypothesis:List the given informationState in statistical and word format the null hypothesis and the alternative hypothesisIdentify the “claim”Determine if the test is one-tailed (left or right) or two-tailedIdentify the critical value for the test (or the stated p-value level at which the test is being conducted)Draw a picture containing the critical value(s) and, after testing, the test statisticIdentify the statistical testConduct the test and obtain the test statistic (place it on your drawing)Analyze your results (relationship between critical value and test statistic (or p-values comparison)State a conclusion. Include a statement of the null hypothesis, the level at which it was tested, and whether it was retained or rejected.NEXT CLASS: TOPICS: Hypothesis Testing; DUE: CA#7Statistics Essentials Hypothesis Testing: Know: 1) how to write hypotheses in statistical format and in written format; 2) what statistical significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s), test statistic, p-value, etc.; 4) how to conduct a hypothesis test and interpret the results.Problem 21.1: (Hypothesis)Doctor Salaries: Is there a doctor in the house? The Bureau of Labor Statistics reported that in May 2009, the mean annual earnings of all family practitioners in the United States was $168,550. A random sample of 55 family practitioners in Missouri that month had mean earnings of $154,590 with a standard deviation of $42,750. Do the data provide sufficient evidence at ??????? to conclude that the mean salary for family practitioners in Missouri is less than the national average?Problem 21.2: (C.I. Proportions)New Year’s Resolution: From a recent survey of 2241 U.S. adults, 29 % of respondents indicated that they had made a resolution to eat healthier. (L&F 7ed p.325, #12 & 21)Determine the number of individuals indicating an intent to eat healthier.Construct a 90% confidence interval for the population proportion.Problem 21.3: (C.I. Small Sample)Commute Time: From a random sample of eight people, the mean commute time to work was 35.5 minutes with a standard deviation of 5.8 minutes. Build a 95% confidence interval about the sample mean, for the population mean. (L&F 7ed p.315, #17)Problem 21.4: (Normal Distribution)Test Scores: Assume the test scores for a large class are normally distributed with a mean of 74 and a standard deviation of 10. (Le p.144, #3.14)Suppose that you received a score of 88. What portion of the class received scores higher than you?Suppose that the instructor wants to limit the number of A grades to 20%. What would be the lowest score for an A?5417820-274320224.18.1900224.18.19STAT 101TOPICS: Hypothesis Testing (One Sample)DOCUMENTS:HANDOUTS: Green #22AVAILABLE ONLINE: Green #22; Hypothesis Testing ppt; STAT EXAM #2 REVIEW SHEETS #1-536893507556500ASSIGNMENT:Text LARSON: Ch. 7, section 7.1 – 7.3Text Problems: p. 367 #1-11, 13, 17, 18, 21-23, 25, 26-69215016129000EX#6 Stat 101 GEAC Course Assessment FormItems below FORMULAS: Hypothesis TestingSteps in testing a hypothesis:List the given informationState in statistical and word format the null hypothesis and the alternative hypothesisIdentify the “claim”Determine if the test is one-tailed (left or right) or two-tailedIdentify the critical value for the test (or the stated p-value level at which the test is being conducted)Draw a picture containing the critical value(s) and, after testing, the test statisticIdentify the statistical testConduct the test and obtain the test statistic (place it on your drawing)Analyze your results (relationship between critical value and test statistic (or p-values comparison)State a conclusion. Include a statement of the null hypothesis, the level at which it was tested, and whether it was retained or rejected.-6921508191500REVIEW SESSION FOR EXAM #2: FRIDAY APRIL 19 FROM 4:30-6 IN FITZ ROOM 105NEXT CLASS: TOPICS: Hypothesis Testing/Review DUE: COURSE ASSESSMENT FORM; EX#6Statistics Essentials Hypothesis Testing: Know: 1) how to write hypotheses in statistical format and in written format; 2) what statistical significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s), test statistic, p-value, etc.; 4) how to conduct a hypothesis test and interpret the results.Problem 22.1: Good credit: The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO credit score is lower than the cutoff of 720. She finds that a random sample of 100 people had a mean FICO score of 703 with a standard deviation of 92. Can the economist conclude that the mean FICO score is less than 720? Use α=.05 level of significance.Problem 22.2: Measuring lung function: One of the measurements used to determine the health of a person’s lungs is the amount of air a person can exhale under force in one second. This is called the forced expiratory volume in one second, and is abbreviated FEV1. Assume the mean FEV1 for 10-year-old boys is 2.1 liters and that the standard deviation is 0.3. A random sample of 100 10-year-old boys who live in a community with high levels of ozone pollution are found to have a sample mean FEV1 of 1.95 liters. Can you conclude that the mean FEV1 in the high-pollution community is less than 2.1 liters? Use the α = 0.05 level of significance.Testing a hypothesis: (format to be used for upcoming exam) 1) Provide a complete list of the GIVEN information:2) State the null and alternative hypotheses in both statistical form and written form AND identify the Claim being made by checking one of the two boxes located at end of the written description. Statistically:In Words:Claim(check one)59753504445000 Ho: ________________Ho: _________________________________________________________ Ha: _________________Ha: _________________________________________________________3) The hypothesis test is (circle one): left-tailed right-tailed two-tailed 4) Identify the Critical Value(s) for the test.C.V. = __________590550063500step 5) EE00step 5) EE284988048895005) Draw a detailed picture displaying the region(s) of retention and rejection of the null hypothesis. Include the location of the Critical Value(s) and Test Statistic (once calculated). Present the formula to be used, determine the Test Statistic and locate the T.S. on the picture.Show Formula, Calculations and test statistic 6) State Formula:Calculations:7) Test Statistic: _____________ (place here and on diagram)8) Analyze: No written response, just review results so you can address step 9).9) Using the format presented in class, state a conclusion for this hypothesis test.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________5080000106045234.23.1900234.23.19STAT 101TOPICS: Hypothesis Testing for Proportions DOCUMENTS:HANDOUTS: Green #23; Exam #2 Take-home Problem AVAILABLE ONLINE: Green #23; NOTE: the take-home problem sheet must be obtained directly from Doc. J. HWK:EXAM #2 TAKE-HOME PROBLEMFORMULAS: Available on prior green handouts THE FINAL THREE DAYS: 4.25 – Exam #24.30 – data collection for Lab #25.2 & 5.7 – Application LabNOTE: Due to space limitations, May 7th class members cannot be accommodated at one of the Mat 2nd time slots.NEXT CLASS: TOPIC: EXAM #2 DUE AT CLASS TIME: Exam #2 Take-home portionStatistics Essentials: Know: 1) how to write hypotheses in statistical format and in written format; 2) what statistical significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s), test statistic, p value, etc.; 4) how to conduct a hypothesis test and interpret the results.EXAM #2 Review Topics:Descriptive Statistics: Obtaining Statistics – Measures of Center & Variation.Measures of Position – five-number summary, modified box plots with associated calculations; skewness; z-score; etc.Correlation & Regression – scatter plots, r, r2, least squares line, calculating regression estimatesNormal distribution – standard normal table, finding areas or z values; non-standard normal data, finding probabilities and variable valuesDistribution of sample means - ,, central limit theorem, problems where n>1Confidence Intervals - ? vs. s, < 30 vs.≥ 30, intervals for proportions, finding and E given interval, Standard Normal table, t-table, determining sample size for means problemsHypothesis Testing – one sample for means and proportionsREFERENCES/STUDY MATERIALSGreen Sheet - Keys onlineYellow Sheet - Keys online (most)Course Review Materials – Additional problems & KEYS for areas since Exam #2 (online Supporting Materials link)Text problemsTopic-based PowerPointsAnatomy of Statistics SheetsEssential Statistics: the first PowerPoint – listing items to knowStatistics Essentials: Review this section of each Green sheet. Can you do these things? PROBLEM 23.1: Curing diabetes: vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that more than 60% of those with diabetes who undergo this surgery will recover from diabetes? Use the α=.05 level of significance.PROBLEM 23.2:High salaries for executives: A Washington Post-ABC News poll conducted in October 2009 surveyed a random sample of 1004 adults in the United States. Of these people, 713 said they would support federal legislation putting limits on the amounts that top executives are paid at companies that receive emergency government loans. One highly paid executive claims that less than 75% of U.S. adults support limits on the amounts that executives are paid.State the appropriate null and alternate pute the test statistic.Using α=.05, can you conclude that the executive’s claim is true?Using α=.01, can you conclude that the executive’s claim is true?PROBLEM 23.3: Environment: In 2008, the General Social Survey asked 1493 U.S. adults to rate their level of interest in environmental issues. Of these, 751 said that they were “very interested.” Does the survey provide convincing evidence that more than half of U.S. adults are very interested in environmental issues? Use the α=.05 level of significance.5361305024 4.25.190024 4.25.19STAT 101TOPICS: Exam #2 DOCUMENTS:HANDOUTS: Green #24 AVAILABLE ONLINE: Green #24HWK:NoneNEXT CLASS: TOPICS: data collection for the final’s week lab. 435483063500UPCOMING CLASS SCHEDULEAPRIL 30: Can you say OREOS?FINALS WEEK:8:30 AM CLASS:THURSDAY MAY 2, 2019LOCATION: Milne Library 102 (computer lab)29368751143000CLASS EXAM TIME: 8:00 – 10:3010:00 AM CLASS: TUESDAY MAY 7, 201940767009525NOTE: College policy holds that the final exam (for us #2) must be retained by the faculty member. To assure that this policy is followed, you may not receive credit (up to 30 points) for participation in the final class lab session without exam two’s return. 020000NOTE: College policy holds that the final exam (for us #2) must be retained by the faculty member. To assure that this policy is followed, you may not receive credit (up to 30 points) for participation in the final class lab session without exam two’s return. LOCATION: Milne Library 305 (computer lab)29044907239000CLASS EXAM TIME: 8:00 – 10:30 2:30 PM CLASS: THURSDAY May 2, 2019LOCATION: Milne Library 305 (computer lab)29368751079500CLASS EXAM TIME: 2:00 – 4:30Finals Class Schedule of Events, etc:Course Evaluation followed byData analysis completed individually or in groups of 2-3 max. Resources: Bring any books, handouts, notes, consultants, etc. that you feel may be of help in the data analysis.-4038607112000-701040889000IF YOU ARRIVE LATE, YOU MUST COMPLETE THE LAB PROJECT ON YOUR OWN.Ah, Statistics…The government are very keen on amassing statistics. They collect them, add them, raise them to the nth power, take the cube root and prepare wonderful diagrams. But you must never forget that every one of these figures comes in the first instance from the village watchman, who just puts down what he damn pleases. [--Comment of an English judge on the subject of Indian statistics; Quoted by Sir Josiah Stamp in _Some Economic Matters in Modern Life_]There are three types of people in this world: Those who can count, and those who can't. [Seen on a bumper sticker]The statistics on sanity are that one out of every four Americans is suffering from some form of mental illness. Think of your three best friends. If they're okay, then it's you. [Rita Mae Brown]I always find that statistics are hard to swallow and impossible to digest. The only one I can remember is that if all the people who go to sleep in church were laid end to end they would be a lot more comfortable. [Mrs. Robert A. Taft]Before the curse of statistics fell upon mankind we lived a happy, innocent life, full of merriment and go, and informed by fairly good judgment. [Hilarie Belloc The Silence of the Sea]5326380-68580254.30.1900254.30.19STAT 101NAME: _________________________________4114800698500TOPICS: Data Collection [6 points]; Exam Review DOCUMENTS:HANDOUTS: Green #25 AVAILABLE ONLINE: Green #25HWK:REVIEW FINAL EXAM DATE AND LOCATION LISTED ON GREEN 24NEXT CLASS: TOPIC: Lab Data Analysis Place your data on this sheetEnter your data into the computer file.Answer the questions below.Leave this form in the three-ringed binder.Data Collection & Entry [3]:Questions: For each of the following items think of the various descriptive and inferential statistics we have explored, generate a question that could be explored during the final class meeting, and what we might learn via that investigation.Example: Normal Distribution: What - Examine the weights of double-stuf cookies (whole or filling) to determine proportion of cookies within a pre-determined weight range. Why – an opportunity determine the consistency of cookie production with regard to weight component.Descriptive tables, graphs & statistics [1]: What: ________________________________________________________________________________________Why: _________________________________________________________________________________________Confidence Intervals [1]:What: ________________________________________________________________________________________Why: _________________________________________________________________________________________Hypothesis Testing [1]:What: ________________________________________________________________________________________Why: _________________________________________________________________________________________THE FINAL GREENBREATHE IN, BREATHE OUT, MOVE ON536130586995264/2 & 4/7/1900264/2 & 4/7/19STAT 101TOPICS: Applications Lab: Oreo & Benton Data Analysis DOCUMENTS: Green #26Stat Essentials (taken from today): A final test of what we know and how to apply it.5294630762000Suggested Paper Format-69532515684500Your document, which is limited to ONE sheet of paper (two-sides), is to contain the following five sections, each of which will be further discussed on the reverse. Please do not use text boxes for your discussion. Specific section content is noted on the reverse.Please separate sections of your paper by using the “side-headings” presented below.NAME(s)STAT 101 Lab DATEIntroduction [4]Written hereDescriptive Analysis [6]:Written here. Include one statistics table containing relevant statistics for all variables.Hypothesis Testing [12]:Oreo Double-Stuff:Hypotheses (Statistical and written forms)t-test table; state critical values if using this approachConclusionBenton Double-Stuff:Hypotheses (Statistical and written forms)t-test table; state critical values if using this approachConclusionConfidence Intervals [4]:Oreo Double-Stuf:Statement of confidence IntervalInterpretation of the interval relative to the population mean.Benton Double-Stuf:Statement of confidence IntervalInterpretation of the interval relative to the population mean.Summary [4]:[1] Briefly note the purpose of the study. [2] In one or two sentences for each of the three statistical reviews above, summarize your findings, perhaps separated by cookie brand.[1] Conclusion: Make a summarizing statement regarding whether or not these two cookie brands’ double-stuf cookies live up to their billing and which appears to be more stuffed. Any recommendations?-53340017208500SPSS - how to do it:The “How To” documentation is available on previous SPSS assignments as well as in the online SPSS manual. Hypothesis Test (One Sample t-test): Analyze > Compare Means > One Sample T Test > move variable to right > enter a Test Value into the lower left cell > Options > set C.L. to specified level > Continue > Ok. [Note: to set alpha go to the Options button] Important Notes: You must enter a test value. If you do not the test assumes a value of 0 (zero), which will undoubtedly result in a significant statistical finding and an incorrect one to boot.SPSS only conducts two-tailed t-tests (a more conservative type test).The t-test results will provide a test statistic value under the “t” AND a p-value under the “sig.” You may interpret your result using either the critical value and test statistics comparison approach or the p-value approach.APPLICATIONS LAB:Data File: OREOS.savLab Objective: To determine if Double-Stuf Oreo and Benton cookies actually have twice the filling of their regular versions (i.e. are they double-stuf).Paper Format: Please present your paper in the following format (include headings), addressing the points mentioned below. (See formatting on the prior page sheet.)------Name(s)Stat 101 Lab #3DateIntroduction [4]:Provide a brief paragraph documenting what you are studying and what types of data analysis you will use. (See Lab Objective above.)-53340022669500Descriptive Statistics [6; 2 Oreo calcs, 2 Benton calcs, 2 analysis]: NOTE: These variables are approximately normally distributed. We are only studying filling weights, so no overall cookie weight data are needed. Be sure you are using the variable beginning with the word “FILLING.”Obtain one STATISTICS table that will allow you to compare Regular Oreo and Benton filling weights to those of Double-Stuf Oreo and Benton filling weights. Determine the percentage more “stuf” there is in double-stuf Oreo and Benton cookies vs. regular size cookies of these brands.Discuss your findings: At a minimum, your response should include a statistics table containing appropriate statistics, the percentages noted above, and a brief discussion of those items, along with which cookie brand’s double-stuf cookies actually appear to be more stuffed.-54102020193000Hypothesis Test [12; 6 Oreo hyp., stats, decision; 6 Benton hyp., stats, decision]:NOTE: Review the SPSS information regarding hypothesis testing. You have to conduct two separate hypothesis tests: one for Oreo Double-Stuf Fillings and one for Benton Double-Stuf Fillings.For Oreos:Determine the value equal to twice the Regular Oreo filling mean weight. Use that value when presenting your hypotheses and as the Test Value in a one sample t-test conducted at the ? = ______ significance level. State the null and alternative hypotheses based upon the assumption that twice the regular filling weight would represent the expected weight for a double-stuf cookie.Determine the statistical significance of the hypothesis test. You may use either the critical value approach, in which case you will need to specify the critical values, OR the p-value approach, for which you will need to state significance level at which you are working and the resulting p-value for the test.Discuss your results for the hypothesis test in the format presented in class, including level of significance, retain/reject determination, and restating of the null hypothesis. Discuss what your decision means for Oreo consumers. Repeat above items for the Benton’s cookies.Confidence Intervals [4; 2 each cookie type]:Construct a _______% confidence interval about the mean filling weight of the Double-Stuf Oreo cookies. Enter the C.I. table and discus what this interval means with respect to the population mean, mu.Repeat prior two steps for Double-Stuf Benton cookies.Summary [4]:A summary containing: A restating of the general purpose of the study.A brief summarization of the findings from the three prior sections (no tables, etc., just the overall finding). An overall conclusion comparing the two cookie brands’ regular vs. “double stuf” cookies based upon the findings. Any recommendations for consumers? ................
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