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MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
A variable of two populations has a mean of 55 and a standard deviation of
36 for one of the populations and a mean of 55 and a standard deviation of 10 for the other population. Complete parts (a) through (c).
a. For independent samples of size 9 and 4, respectively, find the mean and standard deviation of x1−x2. (Assume that the sampling is done with replacement or that the population is large enough.)
The mean of x1−x2 is _________
(Type an integer or a decimal. Do not round.)
The standard deviation of x1−x2 is _________
(Round to four decimal places as needed.)
b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below.
A. No, the variable must be approximately normally distributed on at least one of the two populations for the formulas for the mean and standard deviation of x1−x2to hold, as long as the sampling is done with replacement.
hold regardless of the distributions of the variable on the two populations, as long as the sampling is done with replacement or that the population is large enough.
c. Can you conclude that the variable x1−x2 is normally distributed? Explain your answer.
Choose the correct answer below.
A. No, since x1−x2 must be greater than or equal to 0, the distribution is right skewed, so cannot be normally distributed.
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