In randomized, double-blind clinical trials of a new vaccine, monkeys 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, 115 of 746 subjects in the experimental group (group 1) experienced fever as a side effect. After the second dose, 72 of 627 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? Determine the null and alternative hypotheses. \[ \begin{array}{l} H_{0}: p_{1}=p_{2} \\ H_{1}: p_{1}>p_{2} \end{array} \] Find the test statistic for this hypothesis test. 2.12 (Round to two decimal places as needed.) Determine the P-value for this hypothesis test. (Round to three decimal places as needed.)

Step 1 ：Define the null and alternative hypotheses as follows: \(H_{0}: p_{1}=p_{2}\) and \(H_{1}: p_{1}>p_{2}\).

Step 2 ：The test statistic for this hypothesis test is given as 2.12.

Step 3 ：Calculate the P-value for this hypothesis test. The P-value is the probability that we would observe a test statistic as extreme as the one we calculated, assuming the null hypothesis is true. In this case, the null hypothesis is that the proportions of subjects experiencing fever as a side effect in both groups are equal. The alternative hypothesis is that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2. The test statistic of 2.12 suggests that the observed difference in proportions is 2.12 standard deviations away from the mean difference under the null hypothesis.

Step 4 ：The P-value for this hypothesis test is calculated to be approximately 0.017.

Step 5 ：Final Answer: The P-value for this hypothesis test is \(\boxed{0.017}\).