Suppose 223 subjects are treated with a drug that is used to treat pain and 52 of them developed nausea. Use a 0.05 significance level to test the claim that more than $20 \%$ of users develop nausea. The test statistic for this hypothesis test is 1.24 . (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is 0.108 . (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. A. Fail to reject $\mathrm{H}_{0}$. There is sufficient evidence to warrant support of the claim that more than $20 \%$ of users develop nausea. B. Reject $\mathrm{H}_{0}$. There is not sufficient evidence to warrant support of the claim that more than $20 \%$ of users develop nausea. C. Reject $\mathrm{H}_{0}$. There is sufficient evidence to warrant support of the claim that more than $20 \%$ of users develop nausea. D. Fail to reject $\mathrm{H}_{0}$. There is not sufficient evidence to warrant support of the claim that more than $20 \%$ of users develop nausea. (1) Time Remaining: 04:31:24 Next
Solution
Step 1 ：The question is asking us to perform a hypothesis test to determine if more than 20% of users develop nausea after taking a certain drug. The null hypothesis (H0) is that the proportion of users who develop nausea is equal to 20%, and the alternative hypothesis (H1) is that the proportion is greater than 20%.
Step 2 ：We are given that the test statistic is 1.24 and the p-value is 0.108. The significance level is 0.05.
Step 3 ：We compare the p-value to the significance level to make a decision about the hypotheses. If the p-value is less than the significance level, we reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.
Step 4 ：In this case, the p-value (0.108) is greater than the significance level (0.05), so we fail to reject the null hypothesis. This means that there is not sufficient evidence to support the claim that more than 20% of users develop nausea.
Step 5 ：Final Answer: \(\boxed{\text{D. Fail to reject } H_{0}. \text{ There is not sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.}}\)
