Question

In a clinical trial of a certain​ drug, 28 subjects experience headaches among the 234 subjects treated with the drug. Construct a 99​% ​(Wald) confidence interval estimate for the proportion of treated subjects who experience​ headaches, completing parts​ (a) through​ (d) below.

a. Find the best point estimate of the population proportion.

__ ​(Type an integer or a decimal rounded to three decimal places as​ needed.)

b. Identify the value of the margin of error E.

__ ​(Type an integer or a decimal rounded to three decimal places as​ needed.)

c. Construct the confidence interval. _<p<_ ​(Round to three decimal places as​ needed.)

d. Write a statement that correctly interprets the confidence interval. Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.)

A. There is a __​% chance that the true value of the population proportion of subjects treated with the drug who experience headaches will fall between the confidence​ interval's lower and upper limits.

B. We have __% confidence that the true value of the sample proportion of subjects treated with the drug who experience headaches actually is between the confidence​ interval's lower and upper limits.

C. We have __​% confidence that the true value of the population proportion of subjects treated with the drug who experience headaches actually is between the confidence​ interval's lower and upper limits.

D. __% of sample proportions will fall between the lower and upper limits of the confidence interval

Answer 1

a) Point estimate = 28/234
Point estimate = 0.1197
b) Sample proportion () = 0.1197
Sample size (n) = 234
Confidence interval(in %) = 99
z @ 99% = 2.576
Since we know that

Required confidence interval = (0.1197-0.0546, 0.1197+0.0546)
Required confidence interval = (0.0651, 0.1743)
c) C. We have 99% confidence that the true value of the population proportion of subjects treated with the drug who experience headaches actually is between the confidence​ interval's lower and upper limits.
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