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 } ) = square ) 10, the sample size is 5% of the population size, and the sample (round to one decimal place as needed.) the requirements for testing the hypothesis satisfied

Explanation:

Step1: Calculate \(np_0(1 - p_0)\)

Given \(n = 872\), \(p_0=0.015\)

$$
LATEXBLOCK0
$$

Since \(12.9> 10\)

Step2: Check sample - size condition

The sample size \(n = 872\). Usually, if we assume the population is large (in clinical - trial context, the number of potential drug users is large), \(872\) is less than \(5\%\) of a large population.

Step3: Conclusion on hypothesis - testing requirements

For a one - sample proportion hypothesis test \(H_0:p = p_0\) vs \(H_1:p>p_0\), the requirements are: \(np_0(1 - p_0)\geq10\), the sample is a simple random sample (assumed in clinical - trial sampling), and \(n\leq0.05N\) (where \(N\) is the population size). Since \(np_0(1 - p_0)=12.9>10\) and assuming the sample is a simple random sample and \(n = 872\) is less than \(5\%\) of the population size, the requirements for testing the hypothesis are satisfied.

Answer:

Because \(np_0(1 - p_0)=12.9>10\), the sample size is less than \(5\%\) of the population size, and the sample (assuming it is a simple random sample) the requirements for testing the hypothesis are satisfied.