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Chapter 11: Q.2 (page 479)
Why is a sample proportion generally used to estimate a population proportion instead of obtaining the population proportion directly?
Because obtaining a sample proportion is faster and less expensive than obtaining a population proportion, it is always employed to estimate population proportion.
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Life Support. In , the Terri Schiavo case focused national attention on the issue of withdrawal of life support from terminally ill patients or those in a vegetative state. A Harris Poll of U.S. adults was conducted by telephone on April , Of those surveyed, had experienced the death of at least one family member or close friend within the last years who died after the removal of life support. Find and interpret a confidence interval for the proportion of all U.S. adults who had experienced the death of at least one family member or close friend within the last years after life support had been withdrawn.
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.
What important theorem in statistics implies that, for a large sample size, the possible sample proportions of that size have approximately a normal distribution?
Use your result from Exercise to show that a level confidence interval for the difference between two population proportions that has a margin of error of at most can be obtained by choosing
rounded up to the nearest whole number.
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.
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