Question

suppose 209 subjects are treated with a drug that is used to treat pain and 50 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
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 )

Explanation:

• The null hypothesis \(H_0\) is a statement of equality. In hypothesis testing for a proportion \(p\), when testing a claim about a proportion, the null hypothesis is typically set to the value being compared against. Here, we are comparing against \(p = 0.20\), so \(H_0:p = 0.20\).
• The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for. The claim is “more than 20% of users develop nausea”, which translates to \(p>0.20\) in terms of the proportion \(p\).

Answer:

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