The PACE project (pace.uhs.wisc.edu) at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two weeks was 42.2% in 1999 ( n = 334 ) and 21.2% in 2009 (n = 843).
a. Estimate the difference between the proportions in 1999 and 2009, and interpret.
b. Find the standard error for this difference. Interpret it.
c. Construct and interpret a 95% confidence interval to estimate the true change, explaining how your interpretation reflects whether the interval contains 0.
d. State and check the assumptions for the confidence interval in part c to be valid.