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Independent random samples of 64 observations each are
Chapter 8, Problem 2E(choose chapter or problem)
Problem 2E
Independent random samples of 64 observations each are chosen from two normal populations with the following means and standard deviations:
Letand denote the two sample means.
a. Give the mean and standard deviation of the sampling distribution of
b. Give the mean and standard deviation of the sampling distribution of
c. Suppose you were to calculate the difference between the sample meansFind the mean and standard deviation of the sampling distribution of
d. Will the statisticbe normally distributed? Explain.
Questions & Answers
QUESTION:
Problem 2E
Independent random samples of 64 observations each are chosen from two normal populations with the following means and standard deviations:
Letand denote the two sample means.
a. Give the mean and standard deviation of the sampling distribution of
b. Give the mean and standard deviation of the sampling distribution of
c. Suppose you were to calculate the difference between the sample meansFind the mean and standard deviation of the sampling distribution of
d. Will the statisticbe normally distributed? Explain.
ANSWER:
Solution:
Step 1 of 5:
It is given that from the two Normal populations, two independent samples of 64 observations are chosen.
The mean and standard deviations of the observations in the two samples are given.
Population 1 |
Population 2 |
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Also, it is given that and
denote the two sample means respectively.
Using this data, we have to find the required values.