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 who binge drink is actually lower than the national proportion. In a commissioned study, 340 students are selected randomly from a list of all students enrolled at the college. Of these, 130 admit to having engaged in binge drinking.

The college president is more interested in testing her belief that the proportion of students at her college who engage in binge drinking is lower than the national proportion of 0.41. What is the P-value? (Round your answer to four decimal places.)
P-value =

Answer 1

Given:

X = 130, n = 340, P = 0.41, Q =1-P = 1-0.41 = 0.59

Calculation:

Hypothesis:

Ho: P = 0.41

Ha: P < 0.41

Test statistic:

P-value = 0.1499 ..............Using standard Normal table

Conclusion:

P-value > α, i.e. 0.1499 > 0.05, That is Fail to Reject Ho at 5% level of significance.

Therefore, there is Not sufficient evidence that, the proportion of students at her college who engage in binge drinking is lower than the national proportion of 0.41