Between January and June of 2011, The Gallup survey companyconducted telephone interviews. The interviews were part of theGallup-Healthways Well-Being Index survey. The researchersinterviewed a random sample of adults, aged 18 and older. Theadults lived in all 50 of the U.S. states and in the District ofColumbia. Approximately 500 of the people who were interviewed weremen and 500 were women. The people who were interviewed were askedabout how much and how often they exercise. The researchers askedthese people if they exercise for 30 minutes a day, three or moretimes each week. Among the women, 47.8% answered “Yes†whereas54.8% of the men answered “Yesâ€. The researchers estimated that the95% confidence interval for the true difference between theproportions of all U.S adult women and men who would answer “Yesâ€to the question was between -13.2% and -0.82%.
Part 1. Which of the following statements is the bestinterpretation of the 95% confidence interval?
A. We are 95% confident that, across the United States, menare between 0.82% and 13.2% more likely to exercise for 30 minutesat least 3 times a week than are women.
B. There is between a 0.82% and 13.2% chance that the truepercentage of U.S. men who exercise for 30 minutes at least 3 timesa week is higher than the percentage of women.
C. We are 95% confident that in the U.S, there are between0.82% and 13.2% less women exercising for 30 minutes at least 3times a week than men.
Part 2. Think about the results of the percentage of women andmen in the United States who exercise for 30 minutes at least 3times a week. Which of the following statements are supported bythe poll results?
A. There is no difference between the percentage of women andmen because both sample percents are close to 50%.
B. There is no difference between the percentage of women andmen because the confidence interval includes the -5% level ofsignificance.
C. There is a difference between the percentage of women andmen because the sample percentage for women who said “Yes†is below50%, but above 50% for the sample of men.
D. There is a difference between the percentage of women andmen because the confidence interval does not include 0%.
Part 3. Which of the following statements is the bestinterpretation of the statistical term “95% confidence�
A. 95% of the time that the same methods are used, theinterval estimate will include the true difference between thepercentages for women and men in the United States.
B. Adults from 95% of all the states in the United States wereincluded in the poll that was conducted between January and June of2011.
C. There is a 95% chance that the true percentage of women inthe United States who exercise less often than men is between 0.82%and 13.2%.
D. Between 0.82% and 13.2% of the men in 95% of the states inthe United States exercised more often than women.
