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Math 227 Review for Exam 1 Chapter 1 to 4 We collect these data from 50 male students. Which variable is qualitative (categorical) and which is quantitative?a. eye color b. head circumference c. marital status d. number of cigarettes smoked daily e. number of TV sets at homef. temperatures in Southern California for the past yearg. weather conditions in Southern California in past year2. Identify the following research studies as observational or a controlled experiment. Explain why.a. Data from the Motorcycle Industry Council stated that “Motorcycle owners are getting older and richer.” Data were collected on the ages and incomes of motorcycle owners for the years 1980 and 1998 and then compared. The findings showed considerable differences in the ages and incomes of motorcycle owners for the two years.b. A study conducted at Virginia Polytechnic Institute and presented by Psychology Today divided female athletes into two groups and had the students perform as many sit-ups as possible in 90 seconds. The first group was told only to ‘do your best,’ while the second group was told to try to increase the number of sit-ups they did each day by 10%. After 4 days, the first group averaged 43 sit-ups while the second group averaged 56 sit-ups. The conclusion was that athletes who were given specific goals performed better than those who were not given specific goals.c. A recent study showed that eating garlic can lower blood pressure. Researchers prescribed garlic pills to high blood pressure patients and monitored their results over a 6 month period. These results were then compared to high blood pressure patients who had received a placebo. The doctors administering the pills were not aware of which patients had received the treatment.3. The dot plot below shows the ages for about 108 people in three community college math classes.a. Any age 26 and over is considered unusually high for this sample. How many student ages are considered unusual for this sample? b. What percent of the sample was this? 4. Answer the following questions given the distribution of following exam scores.How many students took the chapter 3 exam?What is the shape of the distribution of exam scores?What was a typical score for this class (center)?What was the typical spread for this class?How many students got at least an 80 on the exam?What percentage of students got at least an 80 on the exam?How many students scored less than an 80 on the exam?What percentage of students scored less than an 80 on the exam?What percentage of students scored below 70 on the exam?Approximately what percentage of students scored from 70 to 90 on the exam?5. Which is true of the data whose distribution is shown? I. The distribution is skewed to the right. II. The mean is smaller than the median. III. We should summarize with mean and standard deviation. 6. Answer the following questions given the distribution of salaries of a random company.428626571500What percentage of employees made a salary of less than $35,000? What percentage of employees made a salary of more than $80,000? 60% of employees made a salary of less than ____________?How many employees made a salary of less than $35,000? 7. All students in the physical education class completed a basketball free-throw shooting event and the highest number of shots made was 32. The next day, the PE teacher realized that he had made a mistake. The best student had actually made 38 shots (not 32). Indicate whether changing the student’s score made each of these summary statistics increase, decrease, or stay about the same: Mean Median Range IQR 8. The mean and median scores of a recent math 075 exam were close to 68%. The instructor decided not to count one score of zero that was from an absent student to get a better representation of the class average and then recalculated the new mean and median. Will the new mean increase, decrease or remain about the same? Explain.Will the new median increase, decrease or remain about the same? Explain.True or false: The overall range increased.True or false: The IQR remained about the same.9. The following boxplots compare the ages of all the Oscar Winners from 1970 to 2001. Use this to answer the following questions.33337502468880Actor 5 Number Summary: 31 , 37.25 , 42.5 , 50.25 , 76Actress 5 Number Summary: 21 , 32 , 35 , 41.5 , 8000Actor 5 Number Summary: 31 , 37.25 , 42.5 , 50.25 , 76Actress 5 Number Summary: 21 , 32 , 35 , 41.5 , 80435292511430Consider the distributions of ages for Oscar winningactors and actresses.50% of winners were below what age? Actor: Actress:75% of winners were below what age? Actor: Actress:75% of winners were above what age? Actor: Actress:25% of winners were above what age? Actor: Actress:00Consider the distributions of ages for Oscar winningactors and actresses.50% of winners were below what age? Actor: Actress:75% of winners were below what age? Actor: Actress:75% of winners were above what age? Actor: Actress:25% of winners were above what age? Actor: Actress:How many outliers are there for each gender and what are they? Actor: Actress:What are the shapes of the distributions? Actor: Actress:Did a typical actor or actress win at a younger age? Explain.What are the IQRs for actors and actresses? Interpret these IQRs.Based on the IQRs, did actors or actresses win at a younger age? Explain.Which data set is more consistent and why?Did actors or actresses win at a younger age? Utilize percentages from the Boxplot of the distributions above to support your answer.10. The following data represent the annual chocolate sales (rounded to nearest billions of dollars) for a sample of seven countries in the world. Round answers to nearest tenths.2, 5, 7, 2, 5, 3, 18 a. Find the mean for the data. Write the answer in a complete sentence in context.b. Calculate the standard deviation: s = (x-x)2n-1 . Write the answer in a complete sentence in context. c. Using this standard deviation, one could then expect typical annual chocolate sales to be between which two values? 11.337756534925Answer the following questions with a letter I, II, III, or IV. Explain your choice in complete sentences for each question. Histograms can be used more than once and some answers might have more than one answer.400000Answer the following questions with a letter I, II, III, or IV. Explain your choice in complete sentences for each question. Histograms can be used more than once and some answers might have more than one answer. A. Which graph would represent a distribution of the ages of math 075 students where there is a high percentage of students who recently graduated high school and very few students who over 50? Explain.B. Name all graphs where the mean would be chosen as the best measure of center. Explain.C. Name all graphs where the IQR (interquartile range) would be chosen as the best measure of spread. Explain.D. Which graph would represent a distribution for the heights of koala bears? Explain.12. The ten top grossing Pixar Animated movies for the US box office up to June 2010 are shown below, in millions of dollars.a. Find the medianb. Find the interquartile range (IQR) and interpret the meaning of the IQR in context.c. Between which two values does a typical movie gross?Movie $MillionsToy Story 192A Bug’s Life 163Toy Story 2 246Monsters, Inc. 256Finding Nemo 340The Incredibles 261Cars 244Ratatouille 206WALL-E 224Up 29313. The following graphs show the distributions of the ages in years of a pre statistics class for students in the Fall of 2014.Note: Age 26 is the first outlier.Descriptive Statistics: Ages Variable Mean StDev Minimum Q1 Median Q3 Maximum IQRAges 21.128 6.812 15.0 18.0 19.0 21.0 98.0 3.0 a. Was this a categorical or quantitative study?b. What is the variable (variables)?c. What is the shape of the distribution in the ages?d. Which measure of typical center is best to use? Mean or Median? Explain.e. Which measure of typical spread is best to use? Standard Deviation or IQR? Explainf. What is the typical center? Complete sentence in context.g. What is the typical spread? Complete sentence in context.h. What ages are considered unusual for this group? Were there any students that were unusually younger or older for this sample?14. According to the data above for the ages, the mean was 21.1 years with a standard deviation of 6.8 years.a. What is the range of ages from one standard deviation below the mean to one standard deviation above the mean?b. What is the range of ages from two standard deviations below the mean to two standard deviations above the mean?c. What is the range of ages from three standard deviations below the mean to three standard deviations above the mean?d. Is the age of 25 years more than one standard deviation above the mean? Show by converting to a z score using the formula .e. There was a 98 old student which is unusual. How unusual is she, highly unusual (z-score above 2) or extremely unusual (z-score above 3)?15. A dietitian is interested in comparing the sodium content of real cheese with the sodium content of a cheese substitute in milligrams and asks you (the statistician) to provide data that supports her belief that cheese substitutes typically contain more sodium. You collect the sodium content of several real cheeses and chees substitutes. Using computer technology, you provide the following box plots and sample statistics. Using the following statistics and graphs, decide whether the dietitian’s belief is correct. Support your decision with the statistics provided. (Include discussion of the shapes, any outliers and the best measures of center and spread to support your decision). -3714751270 N Mean SD Minimum Q1 Median Q3 Maximumreal cheese 8 193.1mg 133.2mg 40mg 56.3mg 200mg 292.5mg 420mg00 N Mean SD Minimum Q1 Median Q3 Maximumreal cheese 8 193.1mg 133.2mg 40mg 56.3mg 200mg 292.5mg 420mg-390525354965 N Mean SD Minimum Q1 Median Q3 Maximumcheese substitute 8 253.8mg 68.6mg 130mg 197.5mg 265mg 305mg 340mg00 N Mean SD Minimum Q1 Median Q3 Maximumcheese substitute 8 253.8mg 68.6mg 130mg 197.5mg 265mg 305mg 340mg16. In the real cheese/cheese substitute boxplots, which type had more variability? 17. Which would have a larger standard deviation? The mile times of the male high school track teams in the U.S. or the mile times of the male participants in the last Olympics?18. In 2007, the mean property crime (per 100,000 people) for the 26 states east of the Mississippi River was 409 with a standard deviation of 193. Assume the distribution was roughly symmetric and unimodal.a. Between which two values would you expect to find about 68% of the crime rates?b. Between which two values would you expect to find about 95% of the crime rates?c. If an eastern state had a violent crime rate of 503 crimes per 100,000 people, would you consider this unusual? Explain.19. When would you choose the median as the best measure of center?20. When would you choose the standard deviation as the best measure of spread?21. Data was collected and a scatterplot was constructed that compared a person’s cholesterol reading and the number of servings of vegetables consumed in a week. a. Would you expect a positive or negative association?b. Identify the explanatory and response variable.c. The correlation coefficient, r is found to be - 0.782. Can it be concluded that increasing the number of servings of vegetables will cause lower cholesterol readings? Explain.d. The researcher found that there was an outlier for a person who ate 500 servings of vegetables in a week. It was discovered that it was a typo and this value was changed to the correct number of 50 servings a week. How will the r value be affected?22. Match each description of a set of measurements to a scatterplot. r = - 0.689, r = .728, r = 0.56223. a. What is extrapolation? b. Why is it important to not extrapolate?24. The following scatterplot compares a women’s height with their weight. Describe the association between height and weight.Assume a linear trend exists. Draw a best fit line and use the line to roughly predict the weight of a women who is 65 inches tall (5 feet, 5 inches).25. The regression equation for predicting a women’s weight based on height (from above) is given by:Predicted weight = -443 + 9.03heighta. Find the predicted weight of a women who is 65 inches tall, if applicable.b. Find the predicted weight of a women who is 59 inches tall, if applicable.c. Interpret the slope in context.d. Interpret the y-intercept in context.e. Computer software computes the r value to be r = 0.881. Interpret the value of the correlation coefficient, r.26. The math department at a particular college wants to investigate the use of the newly developed math tutorial program. They decide to sample students to find out about their participation. Several plans for choosing the sample are proposed. Plan a) Students are divided into groups according to their math level (below average, average, and above average). Then twenty students are selected from each group and interviewed to determine whether they participated in the school's tutorial program.Plan b) Every hundredth student who registers is asked whether they participated in the school's tutorial program.Plan c) Students are divided into groups according to their math level (below average, average, and above average). Then all students in the average and above average groups are chosen and interviewed to determine whether they participated in the school's tutorial program.Plan d) Students are selected to be interviewed to determine whether they participated in the school's tutorial program. The researcher goes to the tutoring room and interviews students as they come in.Plan e) 100 students are chosen according to student ID numbers generated by a computer program.Plan f) Students are mailed a questionnaire to determine whether they participated in the school’s tutorial program.A. Which of the above would be a good method to randomly select students? Why?B. Which of the above methods might result in being biased? Why? C. Name the type of sampling used for each of the above.27. Researchers reported that a newly discovered herb helps lower cholesterol. To test this claim, a study is conducted among 1000 high cholesterol patients. Doctors are told to give their patients either the herb in capsule form or a placebo. The doctors are given the information as to who has been randomly assigned the herb or the placebo. The patients are not aware whether they are being given the herb or the placebo.Identify the following: the samplethe explanatory and response variablesIs the sample also the population? Explain.28. What is the difference between a parameter and a statistic? ................
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