A random sample of 1,496 respondents of a majormetropolitan area was questioned about a number of issues. Whenasked to agree or disagree with the statement “Hand guns should beoutlawed”, 650 respondents agreed. Researchers could thus constructa confidence interval for the proportion of the residents of thismetropolitan area who support banning hand guns (use the 95%confidence level). Use this example to answer questions 19 to23.
19. What’s the proportion of respondents in the sample who agreed“Hand guns should be outlawed”?

20. What would be the Z score(s) associated with theconfidence level used in this example?

21. Based on the sample information, what’s thestandard error?

22. Using the sample information to estimate thepopulation proportion in the example, what’s the margin oferror?

23. What conclusion can we make for thisexample?

According to data from the 2018 General Social Survey(GSS 2018), the average number of years of education of the 2345adults in the U.S. sample is 13.73, with a standard deviation of2.974. Compared to the national average of 13.26 years of educationin 2000, researchers are wondering if the national education levelhad increased during these years. Do a hypothesis testing withα=0.05. Use this example to answer questions 24 to 27.
24. What’s the null hypothesis in this case?
A. The average number of years of education in the U.S. adultpopulation did not change much from 2000 to 2018.
B. The average number of years of education in the U.S. adultpopulation was equal to 13.73 in 2018.
C. The average number of years of education for the GSS 2018 sampleis no different from 13.26, the national average in 2000.
D. The average number of years of education in the U.S. adultpopulation had increased from 2000 to 2018.

25. What’s the alternative hypothesis in thiscase?
A. The average number of years of education in the U.S. adultpopulation had changed since 2000.
B. The average number of years of education for the GSS 2018 sampleis different from 13.26, the national average in 2000.
C. The average number of years of education in the U.S. adultpopulation in 2018 was higher than that in 2000.
D. The average number of years of education in the U.S. adultpopulation had decreased from 2000 to 2018.

26. Which of the following statements about thisexample is correct?
A. This is a two-tailed test and you have two rejectionregions.
B. Since the sample size is large, we cannot use the normaldistribution as the sampling distribution.
C. This is a one-tailed test and the rejection region is on theleft side of the sampling distribution.
D. The rejection region is on the right side of the samplingdistribution.

27. What conclusion can we draw for thisexample?
A. There is no enough evidence to reject the null hypothesis.
B. We can be 90% confident that the average number of years ofeducation in the U.S. adult population had increased since2000.
C. The average number of years of education in the U.S. adultpopulation had increased since 2000.
D. There is a significant difference between 2018 and 2000 in termsof the national education level in the U.S. adultpopulation.

Are U-Albany students more likely to approve guncontrol than adults in the U.S.? According to a research report, ona scale from 1 to 10, the mean approval of gun control in the U.S.is 7.8. The mean approval of gun control in a random sample of 26U-Albany students is 8.3, with the standard deviation of 2.2. Use α= 0.01 for the hypothesis testing. Questions 28 to 32 are based onthis example.
28. What would be the H0 for the example?
A. U-Albany students are equally likely to approve gun control thanadults in the U.S.
B. The likelihood of approving gun control among U-Albany studentsis different from that of the U.S. adults.
C. There is no difference between the 26 U-Albany students and allU.S. adults in terms of their attitudes toward gun control.
D. U-Albany students are less likely to approve gun control thanadults in the U.S.

29. What would be the t critical value(s)?

30. What’s the standard error based on the sampleinformation?

31. What is the t obtained value?

32. What conclusion can we make for thisexample?
A. We cannot reject the null hypothesis that the mean approval ofgun control among the 26 U-Albany students is 8.3.
B. There is no enough evidence to reject the null hypothesis thatthe mean approval of gun control among U-Albany students is8.3.
C. We cannot reject the null hypothesis that the mean approval ofgun control among all U-Albany students is 7.8.
D. We can reject H0 and accept H1 that the mean approval of guncontrol among all U-Albany students is larger than 7.8.

In an election exit poll (N = 1,768), 898 respondentssaid they voted for Candidate A. Is Candidate A going to win theelection (more than 50% of votes needed to win)? Use α = 0.1 for ahypothesis testing. Questions 33 to 38 are based on thisexample.

33. What’s the proportion of respondents in the pollvoted for Candidate A?

34. What would be the H1 for the example?
A. The percentage of respondents in the poll voted for Candidate Ais different from 50%.
B. The proportion of all voters in the election who would vote forCandidate A is more than 0.5.
C. The percentage of respondents in the poll voted for Candidate Ais different from 50.8%.
D. The proportion of all voters in the election who would vote forCandidate A is more than 0.51.

35. What would be the Z critical value(s)?

36. What’s the standard error based on the sampleinformation?

37. What is the Z obtained value?

38. What conclusion can we make for thisexample?

(Optional) Using the International Social SurveyProgram data we find women in the U.S. (N = 654) spend, on average,3.53 hours per day doing housework, with the standard deviation of1.91, and women in Sweden (N = 639) spend, on average, 2.87 hoursper day doing housework, with the standard deviation of 1.85.Researchers want to test whether American women spend more timethan Swedish women on housework? Questions 39 to 42 are based onthis example.
39. What is the null hypothesis?

40. What would be the critical value(s) for α =0.05?

41. What would be the z-obtained value?

42. What conclusion can you make for this example?Briefly explain with statements and numbers.

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