Question

suppose 241 subjects are treated with a drug that is used to treat pain and 54 of them developed nausea. use a 0.05 significance level to test the claim that more than 20% of users develop nausea. identify the test statistic for this hypothesis test. the test statistic for this hypothesis test is 0.93 (round to two decimal places as needed.) identify the p - value for this hypothesis test. the p - value for this hypothesis test is 0.18 (round to three decimal places as needed.) identify the conclusion for this hypothesis test. a. fail to reject ( h_0 ). there is not sufficient evidence to warrant support of the claim that more than 20% of users develop nausea. b. reject ( h_0 ). there is sufficient evidence to warrant support of the claim that more than 20% of users develop nausea. c. reject ( h_0 ). there is not sufficient evidence to warrant support of the claim that more than 20% of users develop nausea. d. fail to reject ( h_0 ). there is sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.

Explanation:

Step1: Hypothesis testing rule

In hypothesis testing, if \(P - value\gt\alpha\) (where \(\alpha\) is the significance level), we fail to reject the null hypothesis \(H_0\). Here, \(\alpha = 0.05\) and the \(P - value=0.18\).

Step2: Conclusion

Since \(0.18>0.05\) (i.e., \(P - value>\alpha\)), we fail to reject the null hypothesis. This means there is not sufficient evidence to support the claim that more than \(20\%\) of users develop nausea.

Answer:

A. Fail to reject \(H_0\). There is not sufficient evidence to warrant support of the claim that more than \(20\%\) of users develop nausea.