Question

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 actually lower than the national proportion. In a commissioned study, 348 students are selected randomly from a list of all students enrolled at the college. Of these, 132 admitted to having engaged in binge drinking.
Reference: Ref 19-4

The college president is more interested in testing her suspicion that the proportion of students at her college that binge drink is lower than the national proportion of .41. Her staff tests the hypotheses H0: p = 0.41, Ha: p < 0.41. Based on the P-value, . . .

A. there is little evidence to support a conclusion that the proportion of students at this particular college that binge drink is lower than the national proportion of 0.41.
B. there is strong evidence that the proportion of students at this college that binge drink is lower than the national proportion of 0.41.
C. our sample is statistically significant and we can reject the null hypothesis.
D. we can't reach any reasonable conclusion because the assumptions necessary for a significance test for a proportion are not met in this case.

Answer 1

Given n=348, phat=132/348= 0.38

The test hypothesis is
Z=(0.38-0.41)/sqrt(0.41*(1-0.41)/348)
= -1.14

The p-value is P(Z< -1.14)=0.1271 (check standard normal table)

Since p-value is larger, we do not reject Ho.

Answer: A. there is little evidence to support a conclusion that the proportion of students at this particular college that binge drink is lower than the national proportion of 0.41.