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. identify the null and alternative hypotheses for this test. choose the correct answer below. a. $h_0: p = 0.20$ $h_1: p > 0.20$ b. $h_0: p = 0.20$ $h_1: p < 0.20$ c. $h_0: p > 0.20$ $h_1: p = 0.20$ d. $h_0: p = 0.20$ $h_1: p
eq 0.20$ identify the test statistic for this hypothesis test. the test statistic for this hypothesis test is. (round to two decimal places as needed.)

Explanation:

Step1: Identify the null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The claim is that more than \(20\%\) (\(p > 0.20\)) of users develop nausea. So, the null hypothesis \(H_0:p = 0.20\) and the alternative hypothesis \(H_1:p>0.20\)

Step2: Calculate the sample proportion \(\hat{p}\)

The sample proportion \(\hat{p}=\frac{x}{n}\), where \(x = 55\) (number of successes, i.e., number of people who developed nausea) and \(n=249\) (sample size). So, \(\hat{p}=\frac{55}{249}\approx0.221\)

Step3: Calculate the test - statistic \(z\)

The formula for the test - statistic \(z\) in a one - sample proportion test is \(z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}\)
Substitute \(p = 0.20\), \(\hat{p}=0.221\), and \(n = 249\) into the formula:

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Answer:

• Hypotheses: A. \(H_0:p = 0.20\), \(H_1:p>0.20\)
• Test statistic: \(0.83\)