Question

suppose 232 subjects are treated with a drug that is used to treat pain and 51 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 0.75
(round to two decimal places as needed.)
identify the p - value for this hypothesis test.
the p - value for this hypothesis test is 0.227
(round to three decimal places as needed.)
identify the conclusion for this hypothesis test.
a. 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. fail to 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 decision rule

In hypothesis testing, if the P - value is greater than the significance level ($\alpha$), we fail to reject the null hypothesis ($H_0$). Here, $\alpha = 0.05$ and the P - value is $0.227$.

Step2: Compare P - value and significance level

Since $0.227>0.05$ (P - value > $\alpha$), we fail to reject the null hypothesis.

Answer:

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