Problem

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 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.
-PropzTest  prop <0.08z=1.736349998p=0.9587490161p^=0.1083032491n=277
B. H0:p0.08
C. H0:p=0.08
D. H0:p<0.08

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, α.
B. Fail to reject the null hypothesis because the P-value is greater than the significance level, α.
C. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α.
D. Reject the null hypothesis because the P-value is less than or equal to the significance level, α.
e. What is the final conclusion?
A. There is sufficient evidence to support the claim that less than 8% of treated subjects experienced headaches.
B. There is not sufficient evidence to warrant rejection of thic claim that less than 8% of treated subjects experienced headaches.
C. There is not sufficient evidence to support the claim that less than 8% of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than 8% of treated subjects experienced headaches.

Answer

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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. H0:p=0.08. 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 8% 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. H0:p=0.08. 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 8% of treated subjects experienced headaches.

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