A certain drug is used to treat asthma. In a clinical trial of the drug, 20 of 2

Question

A certain drug is used to treat asthma. In a clinical trial of the drug, 20 of 258 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 11 % 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. a. Is the test two-tailed, left-tailed, or right-tailed? Right tailed test Left-tailed test Two-tailed test b. What is the test statistic? zequals nothing (Round to two decimal places as needed.) c. What is the P-value? P-valueequals nothing (Round to four decimal places as needed.) d. What is the null hypothesis, and what do you conclude about it? Identify the null hypothesis. A. Upper H 0 : p not equals 0.11 B. Upper H 0 : p less than 0.11 C. Upper H 0 : p greater than 0.11 D. Upper H 0 : p equals 0.11 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, alpha .

B. Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha .

C. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, alpha . D. Reject the null hypothesis because the P-value is less than or equal to the significance level, alpha . e

. What is the final conclusion?

A. There is not sufficient evidence to support the claim that less than 11 % of treated subjects experienced headaches.

B. There is not sufficient evidence to warrant rejection of the claim that less than 11 % of treated subjects experienced headaches.

C. There is sufficient evidence to support the claim that less than 11 % of treated subjects experienced headaches. D. There is sufficient evidence to warrant rejection of the claim that less than 11 % of treated subjects experienced headaches.

Explanation / Answer

We use minitab

Test and CI for One Proportion

Test of p = 0.11 vs p < 0.11

Sample X N Sample p 95% Upper Bound Z-Value P-Value
1 20 258 0.077519 0.104904 -1.67 0.048

Using the normal approximation.

a. Is the test two-tailed, left-tailed, or right-tailed? Right tailed test Left-tailed test Two-tailed test

> Left-tailed test

becuse our claim statement claim that less than 11 % of treated subjects experienced headaches.

b. What is the test statistic? zequals nothing (Round to two decimal places as needed.)

>> -1.67 ( see above output Z -value )

c. What is the P-value? P-value equals nothing (Round to four decimal places as needed.)

>> 0.048

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

>> A. Upper H 0 : p not equals 0.11 B.

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

D. Reject the null hypothesis because the P-value is less than or equal to the significance level .

What is the final conclusion?

C. There is sufficient evidence to support the claim that less than 11 % of treated subjects experienced headaches.

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