Question

in a clinical trial, 16 out of 872 patients taking a prescription drug daily complained of fluike symptoms. suppose that it is known that 1.5% of patients taking competing drugs complain of fluike symptoms. is there sufficient evidence to conclude that more than 1.5% of this drugs users experience fluike symptoms as a side effect at the α = 0.1 level of significance?
because ( np_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:p = 0.015 ) versus ( h_1:p>0.015 ) (type integers or decimals. do not round.)
find the test statistic, ( z_0 ).
( z_0 = 0.81 ) (round to two decimal places as needed.)
find the p - value.
p - value = (round to three decimal places as needed.)

Explanation:

Step1: Determine the type of test

Since \(H_1: p>0.015\), this is a right - tailed test.

Step2: Use the formula for the P - value in a right - tailed z - test

The formula for the P - value in a right - tailed \(z\) - test is \(P - value=P(Z > z_0)\), where \(Z\sim N(0,1)\) and \(z_0 = 0.81\).
We know that \(P(Z>z_0)=1 - P(Z\leq z_0)\).
From the standard normal table, \(P(Z\leq0.81)=0.7910\).

Step3: Calculate the P - value

\(P - value=1 - 0.7910=0.209\)

Answer:

\(0.209\)