STA 2023 Name___________________________________

Fall 2012 UF ID # __________________________________

EXAM 3 Test Form Code A

Instructions: This exam contains 33 Multiple Choice questions. Each question is worth 3 points, for a total of 99 points. One point will be given for bringing your ID to the exam as well as filling in your name, UF ID#, and test code on your scantron correctly. Please select the best answer among the alternatives given. You may write whatever you want on this test, but only the answers bubbled in the scantron sheet will be graded. You must submit the scantron sheet for you to receive a grade on the exam. You must show the copy of the exam to the test room proctors before turning in your scantron. Honor pledge: "On my honor, I have neither given nor received unauthorized aid on this

examination." Signature: _______________________________________________________ Questions 1-2 The p-value for testing Ho: µ = 8 against Ha: µ ≠ 8 is 0.353. 1. What decision can be made using a 0.05 significance level?

a) Reject Ho at 0.05 b) Fail to Reject Ho at 0.05 c) Reject Ha at 0.05 d) Fail to Reject Ha at 0.05

2. What can be said about a 95% confidence interval for µ? a) It would contain 0. b) It would not contain 0. c) It would contain 8. d) It would not contain 8.

Questions 3 – 6 In the beginning of the semester survey, students were asked if they preferred doughnuts or bagels. Do a higher proportion of male college students prefer doughnuts than female college students? Below is the Minitab output. Test and CI for Two Proportions: Pastry, Gender Event = doughnuts Gender X N Sample p Female 59 169 0.349112 Male 34 53 0.641509 Difference = p (Female) - p (Male) Estimate for difference: -0.292397 Test for difference = 0 (vs < 0): Z = -3.88 P-Value = 0.000 Test for difference = 0 (vs not = 0): Z = -3.88 P-Value = 0.000 Test for difference = 0 (vs > 0): Z = -3.88 P-Value = 1.000

3.) What is the correct alternative hypothesis? a) Ha: pf − pm > 0 b) Ha: pf − pm < 0 c) Ha: �̂� − �̂�< 0 d) Ha: �̂� − �̂� > 0

4.) What is the value of the population proportion of males who prefer doughnuts?

a) 0.349 b) 0.641 c) -0.292 d) 0.000 e) Unknown

5.) What is the value of the pooled proportion used in the standard error formula for the

significance test? a) 0.292 b) 0.419 c) 0.495 d) None of the above.

6.) Based on the output above, what do we know about the confidence interval for �� − ��?

a) It would include 0. b) It would not include 0. c) It would include 1. d) It would not include 1.

Questions 7 -8 A significance test about a proportion is conducted using a significance level of 0.05. The test statistic equals 2.58. The p-value is 0.01. (Homework Problem 9.43) 7. If Ho were true, for what probability of a Type I error was the test designed?

a) 0.01 b) 0.05 c) 0.95 d) 0.99

8. If this test results in a decision error, what type of error was it?

a) Type I error b) Type II error c) No error

Questions 9 – 11 Is the “Freshman 15” myth really true? Do college freshman really gain 15 pounds? Five randomly selected college females were asked for their weight at the beginning and end of the first semester. Their data is below. Use weight change = beginning of semester weight minus end of semester weight. 1 2 3 4 5 Beginning of the Semester weight

130 156 142 112 124

End of the Semester weight

127 167 145 114 130

9. State the null and alternative hypothesis.

a) Ho: µd=0 Ha: µd <0 b) Ho: µd=0 Ha: µd >0 c) Ho: µ1-µ2=0 Ha: µ1-µ2>0 d) Ho: µ1-µ2=0 Ha: µ1-µ2<0

10. What would be the appropriate degrees of freedom for this problem?

a) 4 b) 5 c) 9 d) 10

11. What would be the standard error?

a) 11.37 b) 5.17 c) 5.08 d) 2.31 e) 1.034

Questions 12 – 16 Determine what type of statistical test should be used to answer each of the questions below. (You will only use each response one time.)

a) One mean b) Comparing means of dependent samples c) Comparing two independent means d) Comparing two independent proportions e) Comparing proportions of dependent samples

12. What is the typical amount of money that a college student spends on clothes per year? 13. Is there a difference in how much college men and college women spend on clothes? 14. Do female college students typically buy designer clothes more often than male college students? One hundred female college students and one hundred male college students were asked if they typically bought designer clothes or not designer clothes. 15. Are college students spending more this year than last year? One hundred people were asked at the end of last year how much money they have spent on clothing. The same people were then asked again at the end of this year. 16. Have people changed their spending habits in the past two years? In November 2009, four hundred people were asked about the last time that they purchased clothes. Did they pay the entire purchase on a credit card or use some other method besides a credit card? The same people were asked again in November 2011 about the last time that they had purchased clothes. Did they pay for the entire purchase on a credit card or use some other method besides a credit card?

Questions 17 – 20 In the beginning of the semester survey, students were asked how many texts they had sent in the past 24 hours. Is there a difference in the population mean number of texts between those who classify themselves as liberal or conservative? The Minitab output is below. Two-Sample T-Test and CI: Text, Politics Two-sample T for Text Politics N Mean StDev SE Mean conservative 90 68.8 94.3 9.9 liberal 128 77 116 10 Difference = mu (conservative) - mu (liberal) 95% CI for difference: (-36.1, 20.2)

17. What would be the point estimate for �� − ��?

a) -8.2 b) 8.2 c) -0.57 d) 0.57 e) Unknown

18. Complete the following sentence.

“We are 95% confident that the population mean number of text messages for conservatives is a) between 36.1 less and 20.2 less than liberals.” b) between 36.1 more and 20.2 less than liberals.” c) between 36.1 more and 20.2 more than liberals.” d) between 36.1 less and 20.2 more than liberals.”

19. What would be the appropriate hypotheses for this problem?

a.) Ho: µ = 0 vs. Ha: µ≠0 b.) Ho: 0=x vs. Ha: 0≠x c.) Ho: 0=− lc xx vs. Ha: 0≠− lc xx

d.) Ho: 0=− lc µµ vs. Ha: 0≠− lc µµ

e.) Ho: pc-pl = 0 vs. Ha: pc-pl ≠ 0

20. Based on the 95% confidence interval above, what would the p-value be? a) Greater than 0.05 b) Equal to 0.05 c) Smaller than 0.05 d) Cannot be determined

Questions 21 – 23 A study was done to see the impact of exercise and losing weight had on decreasing the risk of heart attacks. One thousand nine hundred people were followed for ten years. Out of the nine hundred who exercised regularly and lost weight (group 1), 37 had heart attacks during that time frame. Out of the one thousand that did exercise regularly (group 2), but didn’t lose weight, 47 had heart attacks.

21. Is this an example of independent or dependent samples?

a) Independent samples b) Dependent samples

22. What is the sample relative risk?

a) 0.8747 b) 1.143 c) 0.787 d) 1.27

23. The 95% confidence interval for the population relative risk is (0.57, 1.33). From this, what

conclusion should we make? a) Because it does not include 0, there is no statistically significant evidence of a difference

in risk of heart attacks for people who exercise regularly and lost weight and those who exercised regularly, but didn’t lose weight.

b) Because it includes 1, there is no statistically significant evidence of a difference in risk of heart attacks for people who exercise regularly and lost weight and those who exercised regularly, but didn’t lose weight.

c) Because it does not includes 0, there is statistically significant evidence of a difference in risk of heart attacks for people who exercise regularly and lost weight and those who exercised regularly, but didn’t lose weight.

d) Because it includes 1, there is statistically significant evidence of a difference in risk of heart attacks for people who exercise regularly and lost weight and those who exercised regularly, but didn’t lose weight.

24. In 2010, the General Social Survey asked 9 Democrats and 4 Republicans how many hours they usually worked a week including all jobs. Use the Minitab output below to answer the following question. Two-Sample T-Test and CI Sample N Mean StDev SE Mean 1 9 39.69 7.76 2.6 2 4 26.9 19.9 10 Difference = mu (1) - mu (2) Estimate for difference: 12.7 95% CI for difference: (-20.0, 45.5) T-Test of difference = 0 (vs not =): T-Value = 1.24 P-Value = 0.303 DF = 3

Besides random sampling, what other assumption needs to be satisfied for the analysis to be valid?

I. Data is categorical. II. Data is quantitative. III. The data for Democrats and the data for Republicans are normally distributed. IV. There are at least 15 successes and 15 failures in each group.

a) I and III

b) II and IV

c) I and IV

d) II and III

e) All of the above.

25. Determine if the following statement is true or false. “Statistical Inference methods using the t distribution are robust to violations of the random sample assumption.”

a) This statement is true. b) This statement is false.

26. Determine if the following statement is true or false. “If a 95% confidence interval for � − � contains only positive numbers, then we can conclude that both µ1 and µ2 are positive.”

a) This statement is true. b) This statement is false.

Question 27 – 30 Did American voters change their voting habits for president between 2008 and 2012? In 2008 and 2012, the same two hundred people were asked if they voted in the presidential election. The results are below. Is there a difference in the population proportion of Americans that voted in 2008 (1) and 2012 (2)?

In 2008

Voted Did not Vote

In

2012

Voted 92 12 104

Did not Vote 21 75 96

113 87 200 Total

27. What is the sample proportion that voted in 2008?

a) 0.515 b) 0.565 c) 0.893 d) Unknown

28.What are the correct null and alternative hypothesis statements for the McNemar test?

a) Ho: p1-p2 = 0 vs. Ha: p1-p2 ≠ 0 b) Ho: �̂1- �̂2 =0 vs. Ha: �̂1- �̂2 ≠0 c) Ho: p = 0 vs. Ha: p > 0 d) Ho: p = 0.5 vs. Ha: p> 0.5 e) Ho: �̂ = 0 vs. Ha: �̂ > 0

29. What is the value of the test statistic for the McNemar Test for this scenario?

a) 1.96 or -1.96 b) 1.57 or -1.57 c) 5.74 or -5.74 d) -1.32 or 1.32 e) 12.92 or -12.92

30. Besides random sampling, what is the other assumption of the test? a) The sample size must be greater than 30. b) The number of people that changed their voting habits must be at least 30. c) There must be at least 30 successes and 30 failures in each group. d) There must be at least 15 successes and 15 failures in each group.

31. A study has a random sample of 20 subjects. The test statistic for testing Ho:µ = 100 versus Ha: µ≠100 is t = 2.40. Find the approximate p-value for the alternative Ha: µ≠100. (Homework problem 9.28)

a) between 0.005 and 0.010 b) between 0.010 and 0.025 c) between 0.010 and 0.020 d) between 0.020 and 0.05

32. Do Americans think that more than 2 children per family is ideal? In 1994, the General Social Survey asked 1302 participants what they thought was the ideal number of children in a family. The sample mean was 2.51 and the standard deviation was 0.87. What would be the test statistic for this problem?

a) 0.000 b) -0.954 c) 0.587 d) 1.96 e) 21.15

33. Has there been a change in the perception of the ideal number of children in the American family? In 1986 (sample 1) and in 2010 (sample 2), the General Social Survey included questions that asked participants, “How many children do you think is the ideal number for a family?”. The Minitab output is below. Sample N Mean StDev SE Mean 1 1440 2.86 1.46 0.038 2 1381 3.14 1.87 0.050 Difference = mu (1) - mu (2) Estimate for difference: -0.2800 95% CI for difference: (-0.4042, -0.1558)

Complete the following sentence

“We are 95% confident that the population mean ideal number of children for 1986 is

a) Higher than in 2010 b) Lower than in 2010 c) Not significantly different from 2010 d) The same as in 2010