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 \hat { p } = 0.0599250936 n = 267 d. what is the null hypothesis, and what do you conclude about it? identify the null hypothesis. ○ a. h₀: p ≠ 0.08 ○ b. h₀: p > 0.08 ○ c. h₀: p = 0.08 ○ d. h₀: p < 0.08

Explanation:

In hypothesis testing for a proportion, the null hypothesis \(H_0\) is a statement of equality. The claim is that less than \(8\%\) (\(p < 0.08\)) of treated subjects experienced headaches. The null hypothesis for a one - sided (left - tailed in this case) test about a proportion is \(H_0:p = p_0\), where \(p_0\) is the proportion in the null - hypothesized value. Here, \(p_0=0.08\).
To decide about the null hypothesis, we compare the \(p\) - value (\(p = 0.1133079204\)) with the significance level \(\alpha=0.01\). Since \(p-\text{value}(0.1133)> \alpha(0.01)\), we fail to reject the null hypothesis.

Answer:

The null hypothesis is \(H_0: p = 0.08\) (Option C). We fail to reject the null hypothesis because the \(p\) - value (\(0.1133\)) is greater than the significance level (\(0.01\)).