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Statistics / Mathematical Statistics with Applications 7 / Chapter 8 / Problem 61E

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

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A small amount of the trace element selenium, from 50 to

Chapter 8, Problem 61E

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QUESTION:

Problem 61E

A small amount of the trace element selenium, from 50 to 200 micrograms (μg) per day, is considered essential to good health. Suppose that independent random samples of n1 = n2 = 30 adults were selected from two regions of the United States, and a day’s intake of selenium, from both liquids and solids, was recorded for each person. The mean and standard deviation of the selenium daily intakes for the 30 adults from region 1 were ̅y1 = 167.1 μg and s1 = 24.3 μg, respectively. The corresponding statistics for the 30 adults from region 2 were ̅y2 = 140.9 μg and s2 = 17.6 μg. Find a 95% confidence interval for the difference in the mean selenium intake for the two regions.

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QUESTION:

Problem 61E

A small amount of the trace element selenium, from 50 to 200 micrograms (μg) per day, is considered essential to good health. Suppose that independent random samples of n1 = n2 = 30 adults were selected from two regions of the United States, and a day’s intake of selenium, from both liquids and solids, was recorded for each person. The mean and standard deviation of the selenium daily intakes for the 30 adults from region 1 were ̅y1 = 167.1 μg and s1 = 24.3 μg, respectively. The corresponding statistics for the 30 adults from region 2 were ̅y2 = 140.9 μg and s2 = 17.6 μg. Find a 95% confidence interval for the difference in the mean selenium intake for the two regions.

ANSWER:

Step 1 of 4

We will use following

Let are data observations from population A with mean and standard deviation and data observations from population B with mean and standard deviation . Then confidence interval for difference between this two means is defined by:

where and are sample mean from population and sample mean from population , respectively.

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