On January 7, 2000, the Gallup Organization released the results of a poll comparing the lifestyles of today with yesteryear. The survey results were based on telephone interviews with a randomly selected national sample of 1,031 adults, 18 years and older, conducted December 20-21, 1999.4
a. The Gallup poll found that 42 percent of the respondents said that they spend less than three hours watching TV on an average weekday. Based on this finding, calculate a 99 percent confidence interval for the proportion of U.S. adults who say that they spend less than three hours watching TV on an average weekday. Based on this interval, is it reasonable to conclude that more than 40 percent of U.S. adults say they spend less than three hours watching TV on an average weekday?
b. The Gallup poll found that 60 percent of the respondents said they took part in some form of daily activity (outside of work, including housework) to keep physically fit. Based on this finding, find a 95 percent confidence interval for the proportion of U.S. adults who say they take part in some form of daily activity to keep physically fit. Based on this interval, is it reasonable to conclude that more than 50 percent of U.S. adults say they take part in some form of daily activity to keep physically fit?
c. In explaining its survey methods, Gallup states the following: "For results based on this sample, one can say with 95 percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 3 percentage points." Explain how your calculations for part b verify that this statement is true.