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 five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is lower 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, 162 admitted to having engaged in binge drinking. Based on a P-value that you have computed to be less than 0.05, which of the following conclusions is reasonable?

a There is strong evidence that the proportion of students at this college that binge drink is lower than the national proportion of 0.41.We can't reach any reasonable conclusion because the assumptions necessary for a significance test for a proportion are not met in this case.
b There is moderate but not strong evidence that the proportion of binge drinking students at this college is lower than the national proportion of 0.41.
c 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.

Answer 1

A P-value less than 0.05 indicates strong evidence against the null hypothesis, suggesting that the proportion of binge-drinking students at the college is lower than the national proportion of 41%.

Step-by-step explanation:

Based on the P-value computed to be less than 0.05, the reasonable conclusion is option (a): There is strong evidence that the proportion of students at this college that binge drink is lower than the national proportion of 0.41. A P-value lower than 0.05 typically indicates that there is statistically significant evidence to reject the null hypothesis. In this case, the null hypothesis likely posited that the proportion of binge drinking students at the college is equal to or greater than the national average, and the alternative hypothesis stated that the proportion is lower. Because the P-value is less than 0.05, the college president has evidence to suggest that the rate of binge drinking on her campus is indeed lower than the national average.