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Consider the following hypothesis test. H 0 : μ d ≤ 0 H a : μ d > 0 The following data are from matched samples taken from two populations. Element Population 1 2 1 21 20 2 28 26 3 18 18 4 20 20 5 26 24 a. Compute the difference value for each element. b. Compute d ¯ . c. Compute the standard deviation s d . d. Conduct a hypothesis test using α = .05. What is your conclusion?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 10.3, Problem 19E
Textbook Problem
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Consider the following hypothesis test.

H 0 : μ d 0 H a : μ d > 0

The following data are from matched samples taken from two populations.

Element Population
1 2
1 21 20
2 28 26
3 18 18
4 20 20
5 26 24
  1. a. Compute the difference value for each element.
  2. b. Compute d ¯ .
  3. c. Compute the standard deviation sd.
  4. d. Conduct a hypothesis test using α = .05. What is your conclusion?

a.

To determine

Find the difference value for each element.

Explanation of Solution

Calculation:

The data represents the matched samples drawn from two populations. Consider the test hypothesis as follows:

H0:μd0Ha:μd>0

The difference values for each of the 5 elements are tabulated below:

Populationd
12
2120

b.

To determine

Find d¯ value.

c.

To determine

Find the standard deviation sd.

d.

To determine

Perform a hypothesis test at α=.05 and conclude.

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