According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and

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 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.

19. 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. The value of the z test statistic for this sample is

A) - 1.16 B) 1.16 C) - 1.19 D) 0.1230

20. 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. The P-value is

A) between 0.05 and 0.10. B) between 0.15 and 0.20. C) between 0.10 and 0.15. D) below 0.05.

21. Which of the following conclusions is reasonable, based on the P-value of the given sample?

A) 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.

D) 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

Q-19

Z=(phat-p0)/sqrt(p0*(1-p0)/n)

=(132/348-0.41)/sqrt(0.41*(1-0.41)/348)

=-1.16

Option-A is the answer

Q-20

p-value=P(Z<-1.16)=0.123

So, option –C is answer

Q-21

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

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