Question

In​ randomized, double-blind clinical trials of a new​ vaccine, infants were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second​ dose,114 of 726 subjects in the experimental group​ (group 1) experienced drowsiness as a side effect. After the second​ dose, 71 of 607 of the subjects in the control group​ (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the a=0.10 level of​ significance?

a. Verify the model requirements. Select all that apply.

A.The sample size is more than​ 5% of the population size for each sample.

B.The samples are independent.

C.The sample size is less than​ 5% of the population size for each sample.

D.The data come from a population that is normally distributed.

E.The samples are dependent.

b. Determine the null and alternative hypotheses.

H0:p1(<,>,=,≠) p2

H1:p1(<,>,=,≠) p2

c. Find the test statistic for this hypothesis test.

d. Determine the​ P-value for this hypothesis test.

e. Interpret the​ P-value.

If the population proportions are (equal, not equal) one would expect a sample difference proportion

(smaller than the absolute value of, greater than the absolute value of, smaller than, greater than) the one observed in about BLANK out of 1000 repetitions of this experiment.

f. State the conclusion for this hypothesis test.

A. Reject H0. There is sufficient evidence to conclude that a higher proportion of subjects in group 1 experienced fever

as a side effect than subjects in group 2 at the a=0.01 level of significance.

B. Do not reject H0. There is not sufficient evidence to conclude that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the a=0.01 level of significance.

C. Do not reject H0. There is sufficient evidence to conclude that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the a=0.01 level of significance.

D. Reject H0. There is not sufficient evidence to conclude that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the a=0.01level of significance.

Answer 1

a)\

B.The samples are independent.

C.The sample size is less than​ 5% of the population size for each sample.

b)

Ho: p1=p2

Ha: p1>p2

c)

	group 1	group 2
x=	114	71
p̂=x/n=	0.1570	0.1170
n =	726	607
estimated prop. diff =p̂1-p̂2    =		0.0401
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.13878
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0190
test stat z=(p̂1-p̂2)/Se =		2.11

d)

P value   =

0.0176

(from excel:1*normsdist(-2.11)

e) If the population proportions are (equal one would expect a sample difference proportion greater than the one observed in about 18 out of 1000 repetitions of this experiment.

f)since p value >0.01

B. Do not reject H0. There is not sufficient evidence to conclude that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the a=0.01 level of significance.