Question

in a clinical trial, 16 out of 872 patients taking a prescription drug daily complained of flulike symptoms. suppose that it is known that 1.5% of patients taking competing drugs complain of flulike symptoms. is there sufficient evidence to conclude that more than 1.5% of this drugs users experience flulike symptoms as a side effect at the α = 0.1 level of significance?
because ( n p _ { 0 } ( 1 - p _ { 0 } ) = 12.9 > 10 ), the sample size is less than 5% of the population size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied (round to one decimal place as needed.)
what are the null and alternative hypotheses?
( h _ { 0 } ) versus ( h _ { 1 } ) (type integers or decimals. do not round)

Explanation:

Step1: Determine the null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for.
Since we want to test if more than \(1.5\%\) (\(p_0 = 0.015\)) of the drug's users experience flu - like symptoms, the null hypothesis is \(H_0:p = 0.015\) and the alternative hypothesis is \(H_1:p>0.015\)

Answer:

\(H_0:p = 0.015\) versus \(H_1:p>0.015\)