Question 7, 11.1.17-T
HW Score: $63.64 \%, 7$ of 11 points
Part 4 of 6
Points: 0 of 1
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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.)
Answer
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
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
