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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Social Networking. A Pew Internet de American Life Project examined Internet social networking. Among a sample of online adults years old, said they use social networking sites. Determine a confidence interval for the percentage of all online adults years old who use social networking sites.
Suppose that you are using independent samples to compare two population proportions.
Fill in the blanks.
a. The mean of all possible differences between the two sample proportions equals the
b. For large samples, the possible differences between the two sample proportions have approximately a distribution.
Offshore Drilling. In the February article "Offshore Drilling Support High as Deepwater Horizon Oil Spill Trial Opens," E. Swanson reported on a HuffPost and YouGov poll that asked Americans what they think about increased offshore drilling for oil and natural gas. Of the U.S, adults surveyed, said that they were opposed. Find a confidence interval for the proportion of all U.S. adults who, at the time, opposed increased offshore drilling for oil and natural gas.
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.
Refer to the study on ordering vegetarian considered in Examples 11.8-11.10.
a. Without making a guess for the observed values of the sample proportions, find the common sample size that will ensure a margin of error of at most for a confidence interval. Hint: Use Exercise 11.133.
b. Find aconfidence interval for if, for samples of the size determined in part (a), of the men and of the women sometimes order veg.
c. Determine the margin of error for the estimate in part (b), and compare it to the required margin of error specified in part (a).
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