Question

suppose 235 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. $h_{0}:p = 0.20$ $h_{1}:p>0.20$ b. $h_{0}:p = 0.20$ $h_{1}:p<0.20$ c. $h_{0}:p>0.20$ $h_{1}:p = 0.20$ d. $h_{0}:p = 0.20$ $h_{1}:p
eq0.20$

Explanation:

Step1: Understand null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of no effect or equality. The alternative hypothesis \(H_1\) is what we are trying to find evidence for.

Step2: Analyze the claim

The claim is “more than 20% of users develop nausea”. In hypothesis testing for a proportion \(p\), the null hypothesis for a proportion test is usually \(p = \) the value in the non - alternative case. Here, the non - alternative case (null) is \(p = 0.20\) (since we are comparing to 20% or \(0.20\)). The alternative hypothesis, because of the “more than” claim, is \(p>0.20\)

Answer:

A. \(H_0:p = 0.20\), \(H_1:p>0.20\)