A certain drug is used to treat asthma. In a clinical trial of the drug, 30 of 277 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 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.
B.
C.
D.
Decide whether to reject the null hypothesis. Choose the correct answer below.
A. Reject the null hypothesis because the P-value is greater than the significance level, .
B. Fail to reject the null hypothesis because the P-value is greater than the significance level, .
C. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, .
D. Reject the null hypothesis because the P-value is less than or equal to the significance level, .
e. What is the final conclusion?
A. There is sufficient evidence to support the claim that less than of treated subjects experienced headaches.
B. There is not sufficient evidence to warrant rejection of thic claim that less than of treated subjects experienced headaches.
C. There is not sufficient evidence to support the claim that less than of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than of treated subjects experienced headaches.
Answer
The null hypothesis for this test is that the proportion of subjects who experienced headaches is equal to 8%, or p = 0.08. This is represented by option C. .
Given the p-value of 0.9587490161, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. This is because the p-value is not less than or equal to the significance level, α. Therefore, the correct answer is B. Fail to reject the null hypothesis because the P-value is greater than the significance level, α.
Finally, since we failed to reject the null hypothesis, there is not sufficient evidence to support the claim that less than 8% of treated subjects experienced headaches. This is represented by option C. There is not sufficient evidence to support the claim that less than of treated subjects experienced headaches.
Steps
Step 1 :The null hypothesis for this test is that the proportion of subjects who experienced headaches is equal to 8%, or p = 0.08. This is represented by option C. .
Given the p-value of 0.9587490161, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. This is because the p-value is not less than or equal to the significance level, α. Therefore, the correct answer is B. Fail to reject the null hypothesis because the P-value is greater than the significance level, α.
Finally, since we failed to reject the null hypothesis, there is not sufficient evidence to support the claim that less than 8% of treated subjects experienced headaches. This is represented by option C. There is not sufficient evidence to support the claim that less than of treated subjects experienced headaches.