Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 22 of 251 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.

c. what is the p - value?
p - value = 0.672
(round to three decimal places as needed.)

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:

Step1: Recall the definition of null hypothesis

In hypothesis testing for a proportion, the null hypothesis \(H_0\) is a statement of equality. When testing a claim about a proportion \(p\), the null hypothesis is of the form \(H_0: p = p_0\), where \(p_0\) is the hypothesized proportion.
Here, the claim is about the proportion of treated subjects experiencing headaches. The hypothesized proportion in the claim (related to the null hypothesis) is \(p = 0.08\) (since the claim is compared to \(8\%=0.08\)).

Step2: Analyze each option

• Option A (\(H_0:p

eq0.08\)) is a two - tailed null hypothesis. But our claim is one - tailed (\(p < 0.08\)), so this is incorrect.

• Option B (\(H_0:p > 0.08\)) is not the standard form of a null hypothesis (null hypothesis is about equality).
• Option C (\(H_0:p = 0.08\)) is correct as it is in the form \(H_0:p=p_0\) where \(p_0 = 0.08\).
• Option D (\(H_0:p < 0.08\)) is a one - tailed alternative hypothesis form (not a null hypothesis, null hypothesis is about equality).

Answer:

C. \(H_0: p = 0.08\)