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On the basis of data provided by a Romac salary survey, the variance in annual salaries for seniors in public accounting firms is approximately 2.1 and the variance in annual salaries for managers in public accounting firms is approximately 11.1. The salary data were provided in thousands of dollars. Assuming that the salary data were based on samples of 25 seniors and 26 managers, test the hypothesis that the population variances in the salaries are equal. At a .05 level of significance, 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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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 11.2, Problem 20E
Textbook Problem
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On the basis of data provided by a Romac salary survey, the variance in annual salaries for seniors in public accounting firms is approximately 2.1 and the variance in annual salaries for managers in public accounting firms is approximately 11.1. The salary data were provided in thousands of dollars. Assuming that the salary data were based on samples of 25 seniors and 26 managers, test the hypothesis that the population variances in the salaries are equal. At a .05 level of significance, what is your conclusion?

To determine

Conduct the hypothesis test that the population variances in the salaries are equal at α=0.05. Explain the conclusion.

Explanation of Solution

Calculation:

The given information is that the sample variance and sample size for seniors in public accounting firms are s12=11.1 and n1=26, respectively. The sample variance and sample size for managers in public accounting firms are s22=2.1  and n2=25, respectively. The significance level is α=0.05.

Salary data for managers represent the first sample and Salary data for seniors represent the second sample.

The hypotheses are given below:

Null hypothesis:

H0:σ12=σ22

Alternative hypothesis:

Ha:σ12σ22

Test statistic:

Software procedure:

Step by step procedure to obtain the test statistic using the MINITAB software:

  • Choose Stat > Basic Statistics > 2 Variance.
  • Under Data, choose sample variance.
  • In First, enter 26 under Sample size.
  • In First, enter 11.1 under variance.
  • In Second, enter 25 under Sample size.
  • In Second, enter 2.1 under variance

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