Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 16 of 267 treated subjects experienced headaches (based on data from the manufacturer). the accompanying calculator display shows results from a test of the claim that less than 8% of treated subjects experienced headaches. use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below. 1-propztest prop < 0.08 z = -1.209122358 p = 0.1133079204 p ^ = 0.0599250936 n = 267 right tailed test b. what is the test statistic? z = -1.21 (round to two decimal places as needed.) c. what is the p - value? p - value = (round to three decimal places as needed.)

Explanation:

Step1: Identify the type of test

Since the claim is \(p < 0.08\), this is a left - tailed test.

Step2: Use the formula for the \(P -\)value in a left - tailed \(z -\)test

For a left - tailed \(z -\)test, the \(P -\)value is \(P(Z<z)\). Given \(z=-1.209122358\).
Using the standard normal distribution table or a calculator, \(P(Z < - 1.209122358)\) is approximately \(0.113\) (rounded to three decimal places).

Answer:

\(P - value=0.113\)