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Chapter 8: Q 8.33 (page 330)
What is meant by saying that a statistical procedure is robust?
It means that procedure is working reasonably well.
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Shoe and Apparel E-Tailers. In the special report "Mousetrap: The Most-Visited Shoe and Apparel E-tailers" (Foonucar News, Vol. 58 . No. 3. p. 18), we found the following data on the average time, in minutes, spent per user per month from January to June of one year for a sample of shoe and apparel retail websites.
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.
Toxic Mushrooms?Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at part per million (ppm). M. Melgar et al. measured the cadmium levels in a random sample of the edible mushroom Bolefus pinicola and published the results in the paper "Influence of Some Factors in Toxicity and Accumulation of Cd from Edible Wild Macrofungi in NW Spain (Journal of Envionmental Science and Health. Here are the data obtained by the researchers.
Find and interpret a confidence interval for the mean cadmium level of all Boletus pinicola mushrooms. Assume a population standard deviation of cadmium levels in Bolefus pinicola mushrooms of .
For a fixed confidence level, show that (approximately) quadrupling the sample size is necessary to halve the margin of error. (Hint: Use Formula 8.2.)
Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean.
Decreasing the sample size while keeping the same confidence level.
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