Statistics for Business and Economics (13th Edition)
Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134648385
Author: MCCLAVE
Publisher: PEARSON
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Textbook Question
Chapter 8, Problem 8.89LM

List the assumptions necessary for each of the following inferential techniques:

  1. a. Large-sample inferences about the difference (μ1μ2) between population means using a two-sample z-statistic
  2. b. Small-sample inferences about (μ1μ2) using an independent samples design and a two-sample t-statistic
  3. c. Small-sample inferences abojt (μ1μ2) using a paired diference design and a single sample t-statistic to analyze the differences
  4. d. Large-sample inferences about the differences (μ1μ2) between binomial proportions using a two-sample z-statistic
  5. e. Inferences about the ratio σ 1 2 σ 2 2 of two population variances using an F-test.

a.

Expert Solution
Check Mark
To determine

To find: The assumptions required for the analysis of the difference of two population means (μ1μ2) using the two sample z-statistic.

Explanation of Solution

For the z-statistic of the difference of two means to be valid, the following assumptions are required.

Requirements for a large sample test for difference of two population means:

  • The samples must be independent and drawn randomly.
  • The sample sizes must be greater than 30 that is n1>30 and n2>30 .

Thus, the requirements must be satisfied for the z-statistic of the difference of two means to be valid.

b.

Expert Solution
Check Mark
To determine

To find: The assumptions required for the analysis of the difference of two population means (μ1μ2) using the two sample t-statistic.

Explanation of Solution

For the t-statistic of the difference of two means to be valid, the following assumptions are required.

Assumptions about the two populations:

  • The variances of both the populations must be equal.
  • The relative frequency distribution of the two populations must be approximately normal.

Assumptions about the two samples:

  • The two samples must be drawn from the desired population independently in a random process.

Thus, the requirements must be satisfied for the t-statistic of the difference of two means to be valid.

c.

Expert Solution
Check Mark
To determine

To find: The assumptions required for the analysis of the paired difference of two population means (μ1μ2) .

Explanation of Solution

For the paired t test of the difference of two means to be valid, the following assumptions are required.

Requirements for a small sample paired difference test:

  • The difference sample must be drawn randomly from the target population of difference.
  • The population of difference must be approximately normal.

Thus, the requirements must be satisfied for the z-statistic of the difference of two means to be valid.

d.

Expert Solution
Check Mark
To determine

To find: The assumptions required for the analysis of the difference of two population proportions (μ1μ2) using the two sample z-statistic.

Explanation of Solution

For the z-statistic of the difference of two population proportions to be valid, the following assumptions are required.

Requirements for a large sample test for difference of two population means:

  • The samples must be independent and drawn randomly from the binomial population.
  • The sample sizes must be large for the normal approximation using the central limit theorem.

Conditions to check large sample for difference of population proportions (p^1p^2) :

  • n1p^115 and n1q^115 .
  • n2p^215 and n2q^215 .

Thus, the requirements must be satisfied for the z-statistic of the difference of two population proportions to be valid.

e.

Expert Solution
Check Mark
To determine

To find: The assumptions required for the analysis of the difference of two population variances using the two sample F-statistic.

Explanation of Solution

For the F-statistic of the difference of two population variances to be valid, the following assumptions are required.

Requirements for a large sample test for difference of two population means:

  • The samples must be independent and drawn randomly.
  • The relative frequency distribution of the two populations must be approximately normal.

Thus, the requirements must be satisfied for the F-statistic of the difference of two population variances to be valid.

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Chapter 8 Solutions

Statistics for Business and Economics (13th Edition)

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