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.

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 0.41.

Her staff tests the hypotheses H0: p = 0.41, Ha: p < 0.41.

The P-value is:

A) between 0.05 and 0.10

B)between 0.025 and 0.05

C) between 0.01 and 0.025

D) below 0.01

Explanation / Answer

Ans:

Sample proportion=162/462=0.351

Test statistic:

z=(0.351-0.41)/sqrt(0.41*(1-0.41)/462)

z=-2.578

p-value=P(z<-2.578)=0.005

p-value is below 0.01

Option D is correct.

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