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Chapter 11: Q.11.7 (page 459)
For what is the phrase "number of failures" an abbreviation?
The number of failures refers to the number of people chosen from a sample without a specific attribute.
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Suppose that you can make reasonably good educated guesses, and , for the observed values of and .
a. Use your result from Exercise to show that a -level confidence interval for the difference between two population proportions that has an approximate margin of error of can be obtained by choosing
rounded up to the nearest whole number. Note: If you know likely ranges instead of exact educated guesses for the observed values of the two sample proportions, use the values in the ranges closest to as the educated guesses.
b. Explain why the formula in part (a) yields smaller (or at worst the same) sample sizes than the formula in Exercise 11.133.
c. When reasonably good educated guesses for the observed values of and can be made, explain why choosing the sample sizes by using the formula in part (a) is preferable to choosing them by using the formula in Exercise 11.133.
In this Exercise, we have given the number of successes and the sample size for a simple random sample from a population. In each case,
a. use the one-proportion plus-four -interval procedure to find the required confidence interval.
b. compare your result with the corresponding confidence interval found in Exercises , if finding such a confidence interval was appropriate.
Obtain a sample size that will ensure a margin of error of at most the one specified.
Margin of error
Confidence level
we have given a likely range for the observed value of a sample proportion
a. Based on the given range, identify the educated guess that should be used for the observed value of to calculate the required sample size for a prescribed confidence level and margin of error.
b. Identify the observed values of the sample proportion that will yield a larger margin of error than the one specified if the educated guess is used for the sample-size computation.
A Wall Street Journal article, titled "Hypertension Drug Linked to Cancer," reported on a study of several types of high-blood-pressure drugs and links to cancer. For one type, called calcium-channel blockers, of elderly patients taking the drug developed cancer. For another type, called beta-blockers, of other elderly patients developed cancer. Find a confidence interval for the difference between the cancer rates of elderly people taking calcium-channel blockers and those taking beta-blockers. Note: The results of this study were challenged and questioned by several sources that claimed, for example, that the study was flawed and that several other studies have suggested that calcium-channel blockers are safe.
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