STATISTICS I FINAL EXAMINATION



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230 East 105th Street Kevin McCarthy – Principal

New York, NY 10029 Dr. Suzy Ort – Assistant Principal Supervision

Tel # (212) 831-1517 Mrs. Marcia Edmonds – Assistant Principal – Student Affairs

Fax # (212) 384-6097

Statistics I

Final Examination

January 2012

Ms. Brady

Name: ________________________________ Date: ________________

Period: _______________________________ Time Studied: _________

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PART I: Matching Column 20 min. 20 points _____

PART II: Multiple Choice 30 min. 15 points _____

PART III: Short Answer 50 min. 45 points _____

PART IV: Critical Thinking 20 min. 10 points _____

PART V: Course Evaluation 30 min. 10 points _____

TOTAL: 2 hours, 30 min. 100 points _____

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PART I: MATCHING COLUMN

20 POINTS

2 POINTS PER QUESTION

In each blank, write the letter of the description that best matches each item.

| |Symmetric |

| |skewed to the left |

| |skewed to the right |

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|2. _____ age |nominal variable |

|_____ race |quantitative variable |

|_____ gender | |

|_____ SAT score | |

|3. _____ 2 nominal variables |a. t-test |

| |b. one-way ANOVA |

|_____ 2 quantitative variables |c. correlation |

| |d. chi-square test |

|_____ 1 nominal variable (2 levels) | |

|1 quantitative variable | |

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|_____ 1 nominal variable (2 or more levels) 1 quantitative variable | |

|4. _____ 75, 76, 73, 68, 77 |low variability |

|_____ 92, 53, 15, 78, 41 |high variability |

|_____ 75, 75, 75, 75, 75 |zero variability |

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|_____ each individual has an equal chance of being |a. convenience sampling |

|chosen for the sample |b. random sampling |

|_____ selection of whichever individuals are easiest to |c. voluntary response sampling |

|reach | |

|_____ the sample includes only individuals who respond | |

|to a general appeal (i.e. call-in, write-in poll) | |

|_____ subjects chosen for a sample cannot be reached or |a. undercoverage |

|refuse to answer (i.e. ring-no-answer, hang up |b. nonresponse |

|calls) |c. response error |

|_____ some groups are left out or certain individuals do not have the opportunity to be chosen|d. processing errors |

|for the sample (i.e. homeless individuals) | |

|_____ the participant gives an incorrect response (i.e. | |

|lies, misremembers) | |

|_____ mistakes in mechanical tasks (i.e. miscalculation, | |

|error in data entry) | |

|7. _____ question phrased with words such as “not,” answer |a. negative wording |

|choices include “disagree” |b. double-barreled question |

|_____ difficult to understand |c. loaded question |

|_____ asks two things at once |d. lack of simplicity |

|_____ persuades people to respond with a certain answer | |

|8. _____ the researcher rejects H0 when its actually false |a. correct decision |

|_____ the researcher rejects H0 when its actually true |b. type I error |

|_____ the researcher accepts H0 when its actually false |c. type II error |

|_____ the researcher accepts H0 when its actually true | |

|9. _____ r = 0.2 |a. no correlation |

|_____ r = -0.8 |b. strong negative correlation |

|_____ r = 0 |c. strong positive correlation |

|_____ r = 0.9 |d. weak negative correlation |

|_____ r = -0.1 |e. weak positive correlation |

|_____ r = 1 |f. perfect negative correlation |

|_____ r = -1 |g. perfect positive correlation |

|10. |a. no correlation |

| |b. strong negative correlation |

| |c. strong positive correlation |

| |d. weak negative correlation |

| |e. weak positive correlation |

| |f. perfect negative correlation |

|______ |g. perfect positive correlation |

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PART II: MULTIPLE CHOICE

15 POINTS

1 POINT PER QUESTION

Circle the best answer

11. Which scatter diagram shows the strongest positive correlation?

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12. Roberta’s Chemistry professor stated that the class mean was 69 and the standard deviation was 2 on the final exam. Roberta’s Physics professor stated that the class mean was 76 and the standard deviation was 10 on the final exam. Which of the following best describes how confident Roberta should be about passing each final exam?

a. She should be confident she passed Chemistry, but not confident that she passed Physics.

b. She should not be confident she passed Chemistry, but confident that she passed Physics.

c. She should not be confident she passed Chemistry and not confident that she passed Physics.

d. She should be confident she passed Chemistry and confident that she passed Physics.

13. What is the goal of the U.S. census?

a. to survey the whole population every 10 years

b. to survey the whole population every 5 years

c. to survey part of the population every 10 years

d. to survey part of the population every 5 years

14. A teacher surveys a class using a face-to-face interview. She asks the students how many times they have cheated on a test. Some students lie by responding “zero.” How might the teacher have prevented students from lying?

a. survey more classes

b. use an anonymous survey method

c. also ask some distracter questions

d. survey the students the day after the test

15. A school wants to add a coed soccer program. To determine student interest in the program, a survey will be taken. In order to get an unbiased sample, which group should the school survey?

a. every third student entering the building

b. every member of the varsity football team

c. every member in Ms. Zimmer’s drama classes

d. every student having a second-period French class

16. In a skewed data set that includes outliers, which is/are fair way(s) to represent the average?

I. The median

II. The mean

III. Drop the outlier(s), then take the mean

a. III, only

b. I and II, only

c. I and III, only

d. I, II, and III

17. In a skewed data set that includes outliers, which is/are fair measure(s) of variability?

I. the range

II. variance

III. standard deviation

a. I, only

b. I and III, only

c. II and III, only

d. I, II, and III

18. Which of the following is/are true about the null hypothesis (H0) and the alternative hypothesis (H1)?

I. H0 states there is no relationship between the variables

II. H1 states that there is a relationship between the variables

III. If H0 is false, then H1 is true

a. II, only

b. III, only

c. I and III, only

d. I, II, and III

19. If 16% of the variance in x is accounted for by y, r could equal:

I. 0.8

II. 0.4

III. -0.4

a. II, only

b. I and II, only

c. II and III, only

d. I, II, and III

20. A positive correlation exists when:

I. As the value of x increases, the value of y increases

II. As the value of x decreases, the value of y decreases

III. As the value of x increases, the value of y decreases

a. II, only

b. I and II, only

c. I and III, only

d. I, II, and III

21. Which of the following is/are true about the marking period 3 correlation research project you conducted in this class?

I. Convenience sampling was used

II. The survey method was group administration

III. There was undercoverage

a. III, only

b. I and II, only

c. I and III, only

d. I, II, and III

22. Which are likely to report the mean rather than the median?

I. Private colleges reporting average SAT scores

II. Public open-enrollment colleges reporting average SAT scores

III. An incumbent politician running for re-election reporting average income

a. II, only

b. I and II, only

c. I and III, only

d. I, II, and III

23. The following results are published in a research paper: r (28) = .437, p < .05. Which of the following is/are true:

I. 28 people were surveyed

II. The critical r = .437

III. There is a significant relationship between the variables

a. II, only

b. III, only

c. I and III, only

d. I, II, and III

24. Which of the following theories could explain why there is a negative correlation between age and number of times in love?

a. Older people have experienced more relationships, so they have loved more people.

b. Females fall in love more easily than males.

c. As they get older, people usually change their definition of love to include less people.

d. Age is just a number; it does not relate to whether or not someone is capable of falling in love.

25. As N increases, the critical r

a. increases

b. decreases

c. remains the same

d. cannot be determined

PART III: SHORT ANSWER

45 POINTS

5 POINTS PER QUESTION

Show work for each question

26. (__/5 points)Drew’s quiz scores are 4, 5, 7, and 8.

Calculate the standard deviation of his quiz scores, to the nearest hundredth.

27. (__/5 points) Rewrite an abstract for your research project. In 120 words or less, summarize your hypothesis and reason, method, results, interpretation and theory.

28. During his time as Mayor of New York City, Rudy Guliani increased the number of police officers and the violent crime rate decreased.

a. (__/2 points) Does this mean increasing the number of police officers caused the drop in the violent crime rate? Explain.

b. (__/3 points) Explain three possible interpretations of the correlation between number of police officers and the violent crime rate.

29.

a. (__/3 points) Explain what the Bradley Effect is and how it could have affected the accuracy of the 2008 Presidential election polls.

b. (__/2 points) Explain what the reverse Bradley Effect is and how it could have affected the accuracy of the 2008 Presidential election polls.

30. (__/5 points) Identify the best and worst investments. Explain.

Stock A

Mean = 13%

SD = 14%

Stock B

Mean = 7%

SD = 14%

Stock C

Mean = 13%

SD = 6%

Stock D

Mean = 7%

SD = 6%

31. Two politicians are running for governor. Politician A is the current governor running for re-election. In a debate, he claimed to help raise the average income in the state to $57,000. Politician B is running against politician A. At the same debate, politician B claims the average income in the state is actually only $46,000.

The next day, a graph of average income in the state is printed in a newspaper. This graph is shown below.

a. (__/1 point) Describe:

• the shape of the graph

• the type of outliers, if any

b. (__/1 point) What effect, if any, do these outliers have:

• on the mean

• on the median

c. (__/1 point) Which number represents:

• the mean

• the median

d. (__/1 point) Which number represents a measure of average income that is:

• biased

• unbiased

e. (__/1 point) Which politician reported an average income that is:

• biased

• unbiased

32. Underline each variable and label each as nominal (and number of levels) or quantitative.

Then, state a significance test that could be used to analyze the data from a study about the two variables.

a. (__/1 point) gender and number of times in love

b. (__/1 point) number of absences per week and GPA

c. (__/1 point) number of items one recycles each week and the number of times one litters each week

d. (__/1 point) race and political party

e. (__/1 point) age and number of reality television shows watched per week

33. For each part, write a survey question in the format of a statement in quotes.

Assume the answer choices are in the format “agree or disagree.”

Topic: The Death Penalty

a. (__/1 point) double-barreled question:

b. (__/1 point) loaded question:

c. (__/1 point) negatively worded question:

d. (__/1 point) question that lacks simplicity:

e. (__/1 point) fair question:

34. State one problem with each study about the 2008 U.S. Presidential Election.

a. (__/1 point) A researcher conducted a survey to determine if voters discriminate against presidential candidates on the basis of race or gender. Participants were asked to respond to the statement “I would not vote for Barack Obama because he is black and I would not vote for Hillary Clinton because she is a woman.”

b. (__/1 point) A study was conducted to determine opinions on John McCain. 200 randomly selected U.S. residents were asked to respond to the statement “John McCain should be elected president because he showed his loyalty to the United States as a prisoner of war.”

c. (__/1 point) To determine opinions on electing a Republican president, the following newspaper advertisement was printed:

Should we elect a Republican president? Cast your vote in this special call-in poll today.

If yes, call 1-900-630-4251. If no, call 1-900-630-4252. [Charge is 99 cents for the first minute.]

d. (__/1 point) A researcher conducted a face-to-face interview with 62 people outside her apartment building in Harlem to determine whether voters preferred Obama or McCain. Participants were asked to respond to the statement, “Do you plan to vote for Obama or McCain for President?”

e. (__/1 point) A survey question was posted on the internet to determine voters opinions on the age of presidential candidates. Participants were asked to respond to the statement “John McCain, age 71, is too old to be president.”

PART IV: CRITICAL THINKING / DATA ANALYSIS

10 POINTS

35. Show work and use the chart of critical values on the following page.

Analyze the data on the following page to determine if there is a relationship between percent of the population with a bachelor’s degree or more and percent unemployed in each state. Round the value for the statistic to the nearest thousandth.

Include:

• (__/2 points) hypothesis and reason

• (__/2 points) calculate a bivariate statistic, to the nearest thousandth

• (__/2 points) significance

• (__/2 points) interpretation and theory

• (__/2 points) write results in research paper format [ r( )… ]

|Hypothesis |Reason |

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|(__/1 point) |(__/1 point) |

|Interpretation |Theory |

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|(__/1 point) |(__/1 point) |

|State |Percent with Bachelors Degree or More (2006) |Percent Unemployed (2007) |

|California |29.0 |5.4 |

|Florida |25.3 |4.0 |

|Indiana |21.7 |4.5 |

|Maine |25.8 |4.7 |

|Mississippi |18.8 |6.3 |

|New Hampshire |31.9 |3.6 |

|New York |31.2 |4.5 |

|North Dakota |25.6 |3.2 |

|Rhode Island |29.6 |5.0 |

|Utah |28.6 |2.7 |

|Wisconsin |25.1 |4.9 |

Source: U.S. Census Bureau, Statistical Abstract of the United States: 2009.

Critical Values of the Correlation Coefficient

|Level of Significance (p) for a Two-Tailed Test |

|df (n-2): |0.05 |

|1 |0.997 |

|2 |0.950 |

|3 |0.878 |

|4 |0.811 |

|5 |0.754 |

|6 |0.707 |

|7 |0.666 |

|8 |0.632 |

|9 |0.602 |

|10 |0.576 |

|11 |0.553 |

|12 |0.532 |

|13 |0.514 |

|14 |0.497 |

|15 |0.482 |

|16 |0.468 |

|17 |0.456 |

|18 |0.444 |

|19 |0.433 |

|20 |0.423 |

|21 |0.413 |

|22 |0.404 |

|23 |0.396 |

|24 |0.388 |

|25 |0.381 |

|26 |0.374 |

|27 |0.367 |

|28 |0.361 |

|29 |0.355 |

|30 |0.349 |

|35 |0.325 |

|40 |0.304 |

|45 |0.288 |

|50 |0.273 |

|60 |0.250 |

|70 |0.232 |

|80 |0.217 |

|90 |0.205 |

|100 |0.195 |

PART V: COURSE EVALUATION

10 POINTS

36. Discuss the bullet points below in an essay.

Paragraph 1:

▪ What did you like about this class?

▪ Explain the strengths and weaknesses of Ms. Brady’s teaching of this course.

▪ How could the class be improved? Please actually list suggestions.

Paragraph 2: Discuss your opinion on each:

▪ Tests and final exam (difficulty and amount of review)

▪ Study strategies (consolidating notes on a folded sheet of colored paper, elimination quizzing by highlighting, working with a partner in a study group)

▪ Homework (weekly, z club, type of assignments)

▪ Real world application and class surveys

▪ Combining math and psychology

▪ Research project (presentations, sticker chart, time to given to complete it)

▪ Grading policy (harsh late work penalties, marking period averages, HW, research project)

Paragraph 3:

▪ Did you give your best effort in this class?

▪ Students are usually placed in remedial math if they don’t get a 75 on the regents or pass the college placement test. Do you think you will have to first take remedial math in college? Why or why not?

▪ Next, students are usually placed in Math 101 / Advanced Algebra. Are you interested in asking your advisor if you can take Statistics for your required college math credit instead? Why or why not?

▪ Discuss your progress in this class (strengths, areas for improvement).

▪ How could you improve next semester?

Name: ___________________ Date: _____________________

Ms. Brady College Statistics I

Course Evaluation

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“SCRAP PAPER”

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