Study of undergraduate problem drinking. In Alcohol & Alcoholism (Jan/Feb. 2007), psychologists at the University of Pennsylvania compared the levels of alcohol consumption of male and female freshman students. Each student was asked to estimate the amount of alcohol (beer, wine, or liquor) they consume in a typical week. Summary statistics for 128 males and 184 females are provided in the accompanying table.
a. For each gender, find a 95% confidence interval for mean weekly alcohol consumption.
b. Prior to sampling, what is the probability that at least one of the two confidence intervals will not contain the population mean it estimates? Assume that the two intervals are independent.
c. Based on the two confidence intervals, what inference can you make about which gender consumes the most alcohol, on average, per week? (Caution: In Chapter 9, we will learn about a more valid method of comparing population means.)