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. The poll asked several questions and compared the 1999 responses with the responses given in polls taken in previous years. Below we summarize some of the poll's results.

Percentage of respondents who

1 Had taken a vacation lasting six days or more within the last 12 months:

December 1999 42% December 1968 62%

2 Took part in some sort of daily activity to keep physically fit:

December 1999 60% September 1977 48%

3 Watched TV more than four hours on an average weekday:

December 1999 28% April 1981 25%

Assuming that each poll was based on a randomly selected national sample of 1,031 adults and that the samples in different years are independent,

a) Let p₁ be the December 1999 population proportion of U.S. adults who had taken a vacation lasting six days or more within the last 12 months, and let p₂ be the December 1968 population proportion who had taken such a vacation. Calculate a 99 percent confidence interval for the difference between p₁ and p₂. Interpret what this interval says about how these population proportions differ.

b) Let p₁ be the December 1999 population proportion of U.S. adults who took part in some sort of daily activity to keep physically fit, and let p₂ be the September 1977 population proportion who did the same. Carry out a hypothesis test to attempt to justify that the proportion who took part in such daily activity increased from September 1977 to December 1999. Use =.05 and explain your result.

c) Let p₁ be the December 1999 population proportion of U.S. adults who watched TV more than four hours on an average weekday, and let p₂ be the April 1981 population proportion who did the same. Carry out a hypothesis test to determine whether these population proportions differ. Use =.05 and interpret the result of your test.