25. Lipitor In clinical trials of the drug Lipitor (atorvastatin), 270 subjects were given a pla- cebo and 7 of them had allergic reactions. Among 863 subjects treated with 10 mg of the drug, 8 experienced allergic reactions. Construct the two 95% confidence interval estimates of the percentages of allergic reactions. Compare the results. What do you conclude?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a
confidence interval estimate of p, then address the given question.
Transcribed Image Text:Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.
25. Lipitor In clinical trials of the drug Lipitor (atorvastatin), 270 subjects were given a pla-
cebo and 7 of them had allergic reactions. Among 863 subjects treated with 10 mg of the drug,
8 experienced allergic reactions. Construct the two 95% confidence interval estimates of the
percentages of allergic reactions. Compare the results. What do you conclude?
Transcribed Image Text:25. Lipitor In clinical trials of the drug Lipitor (atorvastatin), 270 subjects were given a pla- cebo and 7 of them had allergic reactions. Among 863 subjects treated with 10 mg of the drug, 8 experienced allergic reactions. Construct the two 95% confidence interval estimates of the percentages of allergic reactions. Compare the results. What do you conclude?
Expert Solution
Step 1

In this case, the estimated population proportion (i.e., the proportion of subjects with allergic reaction due to placebo and 10g of the drug in this case) confidence interval gives an interval for the considered population proportion, with a certain degree of confidence (i.e., 95%). The CI for the proportion is:

p^±zp^(1-p^)nwhere, p^=sample proportionz=critical valuen=sample size

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