According to the National Institute on Alcohol Abuse and Alcoholism, and the Nat

Question

According to the National Institute on Alcohol Abuse and Alcoholism, and the National Institutes of Health, 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 conclusion is reasonable?

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

Explanation / Answer

The statistical software output for this problem is:

One sample proportion hypothesis test:
p : Proportion of successes
H0 : p = 0.41
HA : p < 0.41

Hypothesis test results:

p - value < 0.05, reject the null hypothesis.

Hence,

Option D is correct.

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 162 462 0.35064935 0.022882156 -2.5937525 0.0047

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