Question

suppose 220 subjects are treated with a drug that is used to treat pain and 54 of them developed nausea. use a 0.10 significance level to test the claim that more than 20% of users develop nausea.
identify the null and alternative hypotheses for this test. choose the correct answer below.
a. ( h_{0}: p = 0.20 )( h_{1}: p
eq 0.20 )
b. ( h_{0}: p > 0.20 )( h_{1}: p = 0.20 )
c. ( h_{0}: p = 0.20 )( h_{1}: p > 0.20 )
d. ( h_{0}: p = 0.20 )( h_{1}: p < 0.20 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is 1.69
(round to two decimal places as needed.)
identify the p - value for this hypothesis test.
the p - value for this hypothesis test is 0.046
(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. fail to reject ( h_{0} ). there is not sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.
c. fail to reject ( h_{0} ). there is sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.
d. reject ( h_{0} ). there is sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.

Explanation:

Step1: Compare P - value and significance level

We are given a significance level \(\alpha = 0.10\) and a P - value \(P=0.046\)

Step2: Make a decision

Since \(P = 0.046<\alpha=0.10\), we reject the null hypothesis \(H_0\)

Answer:

D. Reject \(H_0\). There is sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.