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Chapter 8: Q 8.4. (page 319)
Express the form of most of the confidence intervals that you will encounter in your study of statistics in terms of "point estimate" and "margin of error."
The requires expression is:
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A confidence interval for a population mean has a margin of error of
a. Determine the length of the confidence interval.
b. If the sample mean is , obtain the confidence interval.
c. Construct a graph that illustrates your results.
Explain why the margin of error determines the accuracy with which a sample mean estimates a population mean.
Fuel Tank Capacity. Consumer Reports provides information on new automobiles models-including price, mileage ratings, engine size, body size, and indicators of features. A simple random sample of new models yielded the following data on fuel tank capacity, in gallons.
a. Determine a point estimate for the mean fuel tank capacity of all new automobile models. Interpret your answer in words. (Note: gallons.)
b. Determine a confidence interval for the mean fuel tank capacity of all new automobile models. Assume gallons.
c. How would you decide whether fuel tank capacities for new automobile models are approximately normally distributed?
d. Must fuel tank capacities for new automobile models be exactly normally distributed for the confidence interval that you obtained in part (b) to be approximately correct? Explain your answer.
Wedding Costs. According to Bride's Magazine, getting married these days can be expensive when the costs of the reception, engagement ring, bridal gown, and pictures-just to name a few-are included. A simple random sample of recent U.S. weddings yielded the following data on wedding costs, in dollars.
a. Use the data to obtain a point estimate for the population mean wedding cost. , of all recent U.S. weddings. (Note: The sum of the data is .)
b. Is your point estimate in part (a) likely to equal exactly? Explain your answer.
Keep on Rolling. The Rolling Stones, a rock group formed in the , have toured extensively in support of new albums, Pollstar has collected data on the earnings from the Stones's North American tours. For thirty randomly selected Rolling Stones concerts, the mean gross earnings is million. Assuming a population standard deviation gross earnings of million, obtain a confidence interval for the mean gross earnings of all Rolling Stones concerts. Interpret your answer in words.
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