Problem
Question 7, 11.1.17-T HW Score: $63.64 \%, 7$ of 11 points Part 4 of 6 Points: 0 of 1 Save In randomized, double-blind clinical trials of a new vaccine, rats 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, 108 of 713 subjects in the experimental group (group 1) experienced drowsiness as a side effect. After the second dose, 65 of 594 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 $\alpha=0.10$ level of significance? \[ \begin{array}{l} H_{0}: p_{1}=p_{2} \\ H_{1}: p_{1}>p_{2} \end{array} \] Find the test statistic for this hypothesis test. 2.23 (Round to two decimal places as needed.) Determine the P-value for this hypothesis test. 0.013 (Round to three decimal places as needed.) Interpret the P-value. If the population proportions are one would expect a sample difference proportion the one observed in about 10 out of 1000 repetitions of this experiment. (Round to the nearest integer as needed.)
Solution
Step 1 ：State the null and alternative hypotheses: \(H_{0}: p_{1}=p_{2}\) and \(H_{1}: p_{1}>p_{2}\)
Step 2 ：Calculate the test statistic for this hypothesis test, which is 2.23
Step 3 ：Determine the P-value for this hypothesis test, which is 0.013
Step 4 ：Interpret the P-value: If the population proportions are equal, one would expect a sample difference as extreme as the one observed in about 13 out of 1000 repetitions of this experiment
Step 5 ：Final Answer: If the population proportions are equal, one would expect a sample difference as extreme as the one observed in about \(\boxed{13}\) out of 1000 repetitions of this experiment
