STATISTICS 115-In a clinical trial of a vaccine, 10,000 children

1. In a clinical trial of a vaccine, 10,000 children were randomly divided into two groups. The subjects in group 1 (the experimental group) were given the vaccine while the subjects in group 2 (the control group) were given a placebo. Of the 5,000 children in the experimental group, 81 developed the disease. Of the 5,000 children in the control group,

115 developed the disease.

Determine whether the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group who contracted the disease at the ? = 0.01 level of significance.

Choose the correct null and alternative hypotheses below.

A.

H0 : p1 = p2 versus H1 : p1 ? p2

B.

H0 : p1 = p2 versus H1 : p1 < p2

C.

H0 : p1 = p2 versus H1 : p1 > p2

D. H0 : p1 = 0 versus H1 : p1 < 0

Determine the test statistic.

z0 = (Round to two decimal places as needed.) Determine the P-value.

The P-value is . (Round to three decimal places as needed.)

What is the result of this hypothesis test?

A.

Do not reject the null hypothesis because there is not sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at ? = 0.01.

B.

Reject the null hypothesis because there is not sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at ? = 0.01.

C.

Reject the null hypothesis because there is sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at ? = 0.01.

D. Do not reject the null hypothesis because there is sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at ? = 0.01.

2. A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained if he wishes the estimate to be within two percentage points with 90% confidence, assuming that

(a)he uses the estimates of 22.7% male and 19.3% female from a previous year?

(b)he does not use any prior estimates?

(a)n = (Round up to the nearest whole number.)

(b)

n = (Round up to the nearest whole number.)