Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 26 of 292 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 0.05 significance level to complete parts (a) through (e) below. 1-propztest prop < 0.08 x = 0.569473598 p = 0.7154836085 p = 0.0890410959 n = 292 d. h₀: p ≠ 0.08 decide whether to reject the null hypothesis. choose the correct answer below. a. fail to reject the null hypothesis because the p - value is less than or equal to the significance level, α. b. fail to reject the null hypothesis because the p - value is greater than the significance level, α. c. reject the null hypothesis because the p - value is greater than the significance level, α. d. reject the null hypothesis because the p - value is less than or equal to the significance level, α.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \( P - value\leq\alpha\), reject \(H_0\). If \(P - value>\alpha\), fail to reject \(H_0\). Here, \(\alpha = 0.05\).

Step2: Identify the \(P - value\) from the calculator display

From the calculator display, \(P - value=0.569473598\)

Step3: Compare the \(P - value\) with \(\alpha\)

Since \(0.569473598>0.05\) (i.e., \(P - value>\alpha\))

Answer:

B. Fail to reject the null hypothesis because the P - value is greater than the significance level, \(\alpha\).