According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 41% of college students nationwide engage in "binge drinking" behavior, having 5 or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is greater than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 219 admitted to having engaged in binge drinking. Use a significance level of 0.05
a. What is the question of interest?
b. State the null and alternative hypotheses.
c. Check the conditions for inference.
d. Calculate the test statistic. Show work!
e. Give the appropriate p-value and state whether it is one-sided or two-sided.
f. Calculate the appropriate 95% confidence interval. Show work!
g. Using the results from parts e and f, summarize your conclusions to the university. Interpret the CI and results of your test. Use the four part conclusion method.