Question

suppose 249 subjects are treated with a drug that is used to treat pain and 55 of them developed nausea. use a 0.05 significance level to test the claim that more than 20% of users develop nausea. the p - value for this hypothesis test is (round to three decimal places as needed.) identify the conclusion for this hypothesis test. a. reject $h_0$. there is sufficient evidence to warrant support of the claim that more than 20% of users develop nausea. b. fail to reject $h_0$. there is suffi ent 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. reject $h_0$. there is not sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.

Explanation:

Step1: Calculate sample proportion

The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 55$ and $n=249$. So, $\hat{p}=\frac{55}{249}\approx0.221$.

Step2: State hypotheses

The null hypothesis $H_{0}:p = 0.20$ and the alternative hypothesis $H_{1}:p>0.20$.

Step3: Calculate test - statistic

The test - statistic for a proportion is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$. Substitute $p = 0.20$, $\hat{p}=0.221$, and $n = 249$.

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Step4: Find P - value

Since it is a right - tailed test ($H_{1}:p>0.20$), the P - value is $P(Z>z)$. Using the standard normal table, $P(Z > 0.83)=1 - P(Z\leq0.83)$. From the standard normal table, $P(Z\leq0.83)=0.7967$. So, $P(Z>0.83)=1 - 0.7967 = 0.203$.

Step5: Make a decision

Compare the P - value with the significance level $\alpha = 0.05$. Since $P - value=0.203>0.05$, we fail to reject $H_{0}$.

Answer:

The P - value is $0.203$.
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.