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On the basis of data provided by a salary survey, the variance in annual salaries for seniors in public accounting firms is approximately 2.3 and the variance in annual salaries for managers in public accounting firms is approximately 12.3. 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 to determine whether there is a significant difference between the variances of salaries for seniors and managers. At a 0.05 level of significance, what is your conclusion?

Respuesta :

Answer:

We conclude that there is a significant difference between the variances of salaries for seniors and managers.

Step-by-step explanation:

We are given the following in the question:

[tex]s_1^2 = 2.3, n_1 = 25\\s_2^2 = 12.3, n_2 = 26[/tex]

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

[tex]H_{0}: \sigma_1^2 = \sigma_2^2\\H_A: \sigma_1^2 \neq \sigma_2^2[/tex]  

We use F-test to determine the difference in variation between the two samples.

Formula:

[tex]F_{stat} = \displaystyle\frac{s_2^2}{s_1^2}\\\\(As ~s_2 > s_1)[/tex]

Putting all the values, we have

[tex]F_{stat} = \displaystyle\frac{12.3}{2.3} = 5.3478[/tex]  

Now we calculate the p-value at degree of freedom(26-1 = 25, 25-1 = 24)

P-value = 0.000053

Since the p value is less than the significance level, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Thus, we conclude that there is a significant difference between the variances of salaries for seniors and managers.

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