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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich
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Independent random samples were selected from each of two

Chapter 8, Problem 78E

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QUESTION:

Problem 78E

Independent random samples were selected from each of two normally distributed populations, n1 = 12 from population 1 and n2 = 27 from population 2. The means and variances for the two samples are shown in the table.

a. Test the null hypothesis against the alternative hypothesis . Use α = .10.

b. Find and interpret the approximate p-value of the test.

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QUESTION:

Problem 78E

Independent random samples were selected from each of two normally distributed populations, n1 = 12 from population 1 and n2 = 27 from population 2. The means and variances for the two samples are shown in the table.

a. Test the null hypothesis against the alternative hypothesis . Use α = .10.

b. Find and interpret the approximate p-value of the test.

ANSWER:

Step 1 of 4

a)  Let  be the variance of population l and , be the variance of population 2.

Here we have following summary data.

Sample 1

Sample 2

          Size

 = 12

 = 27

         Mean

= 31.7

= 37.4

Standard deviation

= 3.87

= 8.75

Here we set up the null and alternative hypotheses as follows:

Versus

This is a two-tailed test.

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