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Chapter 11: Q. 11.115 (page 477)
Buckling Up. Refer to Exercise and find and interpret a confidence interval for the difference between the proportions of seat-belt users for drivers in the age groups years and 25-69 years.
There is interval for the difference between the proportion is (-0.0937,-0.0063)
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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.
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.
Explain the relationships among the sample proportion, the number of successes in the sample, and the sample size.
A poll by Gallup asked, "If you won million dollars in the lottery, would you continue to work or stop working?' Of the American adults surveyed, said that they would continue working. Obtain a confidence interval for the proportion of all American adults who would continue working if they won 10 million dollars in the lottery.
In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: "... we should be aware that, if the observed value of is closer to than is our educated guess, the margin of error will be larger than desired." Explain why.
One-Proportion Plus-Four z-Interval Procedure. To obtain a plus four -interval for a population proportion, we first add two successes and two failures to our data (hence, the term "plus four") and then apply Procedure on page to the new data. In other words, in place of (which is ), we use . Consequently, for a confidence level of , the endpoints of the plus-four -interval are
As a rule of thumb, the one-proportion plus-four -interval procedure should be used only with confidence levels of or greater and sample sizes of or more.
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