“Smartest People Often Dumbest About Sunburns” is the headline of an article that appeared in the San Luis Obispo Tribune (July 19, 2006). The article states that “those with a college degree reported a higher incidence of sunburn than those without a high school degree—43% versus 25%.” Suppose that these percentages were based on independent random samples of size 200 from each of the two groups of interest (college graduates and those without a high school degree).
a. Are the sample sizes large enough to use the large-sample confidence interval for a difference in population proportions?
b. Estimate the difference in the proportion of people with a college degree who reported sunburn and the corresponding proportion for those without a high school degree using a 90% confidence interval.
c. Is zero included in the confidence interval? What does this suggest about the difference in the two population proportions?
d. Interpret the confidence interval in the context of this problem.