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, 111 of 714 subjects in the experimental group (group 1) experienced fever as a side effect. after the second dose, 68 of 595 of the subjects in the control group (group 2) experienced fever as a side effect. does the evidence suggest that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the \\( \alpha = 0.05 \\) level of significance?
interpret the p - value
if the population proportions are equal, one would expect a sample difference proportion greater than the one observed in about 15 out of 1000 repetitions of this experiment (round to the nearest integer as needed.)
state the conclusion for this hypothesis test.
a. reject \\( h_0 \\). 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 \\( \alpha = 0.05 \\) level of significance.
b. do not reject \\( h_0 \\). 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 \\( \alpha = 0.05 \\) level of significance.
c. reject \\( h_0 \\). 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 \\( \alpha = 0.05 \\) level of significance.
d. do not reject \\( h_0 \\). 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 \\( \alpha = 0.05 \\) level of significance.

Explanation:

In hypothesis testing, if the P - value is less than the significance level ($\alpha$), we reject the null hypothesis ($H_0$). Here, the P - value interpretation implies a relatively low probability (about 15 out of 1000) of observing the sample difference if the population proportions are equal. Since $\alpha = 0.05$ (which is 50 out of 1000), and 15 < 50 (i.e., P - value < $\alpha$), we reject $H_0$.

Answer:

A. Reject $H_0$. 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 $\alpha = 0.05$ level of significance.