Question

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 21 of 274 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 12​% 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.

a. Is the test​ two-tailed, left-tailed, or​ right-tailed?

b. What is the test​ statistic? ​(Round to two decimal places as​ needed.)

z = ?

c. What is the​ P-value? (Round to four decimal places as​ needed.)

d. What is the null​ hypothesis, and what do you conclude about​ it?

A.H0: p≠0.12

B.H0: p=0.12

C.H0: p>0.12

D.H0: p < 0.12

Decide whether to reject the null hypothesis. Choose the correct answer below.

A. Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, alphaα.

B.Fail to reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, alphaα.

C.Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level,alphaα.

D.Reject the null hypothesis because the​ P-value is greater than the significance​ level, alphaα.

e. What is the final​ conclusion?

A. There is not sufficient evidence to warrant rejection of the claim that less than 12​% of treated subjects experienced headaches.

B.There is not sufficient evidence to support the claim that less than 12​% of treated subjects experienced headaches.

C.There is sufficient evidence to warrant rejection of the claim that less than 12​% of treated subjects experienced headaches.

D.There is sufficient evidence to support the claim that less than 12​% of treated subjects experienced headaches.

Answer 1

This is left tailed test, for α = 0.05

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.0766 - 0.12)/sqrt(0.12*(1-0.12)/274)
z = -2.21

P-value = 0.0136

Null Hypothesis, H0: p = 0.12

C.Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level,alphaα.

D.There is sufficient evidence to support the claim that less than 12​% of treated subjects experienced headaches.