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Chapter 8: Q 8.17RP. (page 347)
A random sample of size is taken from a population. A normal probability plot of the sample data shows no outliers but has significant curvature. The population standard deviation is unknown.
The confidence interval can neither be obtained from any procedures.
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We provide a sample mean, sample size, and population standard deviation. In each case, perform the following tasks.
a. Find a 95% confidence interval for the popularion mean. (Note: You may want to review Example 8.2, which begins on page 316.)
b. Identify and interpret the margin of error:
c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.
where,
Preliminary data analyses indicate that you can reasonably apply the z- interval procedure
Poverty and Dietary Calcium. Calcium is the most abundant mineral in the human body and has several important functions. Most body calcium is stored in the bones and teeth, where it functions to support their structure. Recommendations for calcium are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences. The recommended adequate intake (RAI) of calcium for adults (ages ) is milligrams (mg) per day. A simple random sample of adults with incomes below the poverty level gave the following daily calcium intake
Explain why there is more variation in the possible values of the studentized version of than in the possible values of the standardized version of
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.
The margin of error is also called the maximum error of the estimate. Explain why.
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