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Chapter 8: Q 8.59 (page 331)
The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
The given statement is True.
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Class Project: Gestation Periods of Humans. This exercise can be done individually or, better yet, as a class project. Gestation periods of humans are normally distributed with a mean of days and a standard deviation of 16 days.
a. Simulate samples of nine human gestation periods each.
b. For each sample in part (a), obtain a confidence interval for the population mean gestation period.
c. For the confidence intervals that you obtained in part (b), roughly how many would you expect to contain the population mean gestation period of days?
d. For the confidence intervals that you obtained in part (b), determine the number that contain the population mean gestation period of days.
e. Compare your answers from parts (c) and (d), and comment on any observed difference.
Fuel Expenditures. In estimating the mean monthly fuel expenditure, , per household vehicle, the Energy Information ministration takes a sample of size . Assuming that . determine the margin of error in estimating at the level of confidence.
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.
Suppose that a simple random sample is taken from a normal population having a standard deviation of for the purpose of obtaining a confidence interval for the mean of the population.
a. If the sample size is , obtain the margin of error.
b. Repeat part (a) for a sample size of
c. Can you guess the margin of error for a sample size of ? Explain your reasoning.
A variable of a population has a normal distribution. Suppose that you want to find a confidence interval for the population mean.
a. If you know the population standard deviation, which procedure would you use?
b. If you do not know the population standard deviation, which procedure would you use?
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