A certain drug is used to treat asthma. In a clinical trial of the drug, 21 of 2

Question

A certain drug is used to treat asthma. In a clinical trial of the drug, 21 of 279 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from atest of the claim that less than 9% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distrib significance level to complete parts (a) through (e) below 1-PropZTest propk 0.09 z=-0.859800651 p-0.1949494702 p-0.0752688172 n 279 ution and assume a 0.01 a. Is the test two-tailed, left-tailed, or right-tailed? O Right tailed test Left-tailed test O Two-tailed test b. What is the test statistic? ZE Round to two decimal places as needed.) c. What is the P-value? P-value = (Round to four decimal places as needed.) d. What is the null hypothesis, and what do you conclude about it? Identify the null hypothesis. O A. Ho: p 0.09 OD. Ho: P-0.09 Decide whether to reject the null hypothesis. Choose the correct answer below. O A. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, a. B. 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 greater than the significance level, ? O D. Reject the null hypothesis because the P-value is less than or equal to the significance level, a e. What is the final conclusion? A. 0 B. C. 0 D. There is sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches. There is sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches. There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches. There is not sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced

Explanation / Answer

Data given to us is as follows:

Sample size n = 279

Sample proportion p' = 21/279 = 0.075

The hypotheses are:

H0: p = 0.09

Ha: p < 0.09

First we calculate standard error:

S = (p'*(1-p')/n)^0.5 = (0.075*(1-0.075)/279)^0.5 = 0.0157

Now we calculate test statistic:

z = (p'-0.09)/S = (0.075-0.09)/0.0157 = -0.955

The p-value for this z-value is:

p = 0.1698

Given significance level a = 0.01

Since this is a left tailed test, so we compare p with a.

Since p > a, we cannot reject the null hypothesis.

So,

There is not sufficient evidence to support the claim that less than 9% of the treated people experienced headaches.

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