Question

We sampled a group of undergraduate students (n=1200) to determine the proportion of students who were considered binge drinkers. We hypothesized that the proportion of students who were binge drinkers were less than the national proportion of college students who were binge drinkers (pnull=0.35).

1. What are the appropriate null and alternative hypotheses?

2. Among the 1200 students sampled, the proportion of binge drinkers (p^) was 0.27. With a one sample z-test, our calculated z was -5.67 and the theoretical z was -1.645. With an alpha of 0.05, we:

a. do no have enough evidence to suggest that the proportion of binge drinkers is less than the national average.

b. have statistically significant evidence to show that the proportion of students who are binge drinkers is less than the national proportion of students are binge drinkers

c. we do not have enough information.

3. We calculated a 95% CI around the sample proportion. The 95% CI is (.247, .293). Based on the CI, we can

a. reject the null hypothesis

b. fail to reject the null hypothesis

c. this cannot be determined based on info given

Answer 1

Claim: The proportion of students who were binge drinkers were less than the national proportion of college students who were binge drinkers.

1) HYPOTHESIS:

The hypothesis is given by,

(That is, the proportion of students who were binge drinkers were greater than or equal to 0.35 (the national proportion of college students who were binge drinkers))

(That is, the proportion of students who were binge drinkers were less than 0.35 (the national proportion of college students who were binge drinkers))

2) GIVEN:

Among the 1200 students sampled, the proportion of binge drinkers . With a one sample z-test, our calculated z was and the theoretical z was .

LEVEL OF SIGNIFICANCE:

DECISION RULE:

CONCLUSION:

The correst answer is Option (b):

Since the calculated z statistic (-5.67) is less than -1.645, we reject the null hypothesis and conclude that we have statistically significant evidence to show that the proportion of students who are binge drinkers is less than the national proportion of students are binge drinkers.

3) GIVEN:

We calculated a 95% CI around the sample proportion. The 95% CI is .

SOLUTION:

HYPOTHESIS:

The hypothesis is given by,

(That is, the proportion of students who were binge drinkers were greater than or equal to 0.35 (the national proportion of college students who were binge drinkers))

(That is, the proportion of students who were binge drinkers were less than 0.35 (the national proportion of college students who were binge drinkers))

CONCLUSION:

The 95% CI is .

Since the value specified by the null hypothesis (0.35) is not in the 95% confidence interval , the null hypothesis can be rejected at the 0.05 level and can be concluded that the proportion of students who were binge drinkers were less than 0.35 (the national proportion of college students who were binge drinkers).

The correct answer is Option (a): reject the null hypothesis.