Question

Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams, with the following results:

Mean Grade Standard Deviation
Professor 1 79.3 22.4
Professor 2 82.1 12.0
What is the alternate hypothesis?

Answer 1

Alternative hypothesis:

`\mathbf{H_a = \sigma_1^2 \\e \sigma_2^2}`

Explanation:

Given that:

Sample 1:

Sample size
`n_1` = 10

Sample mean
`\overline x_1` = 79.3

Standard deviation
`\sigma_1` = 22.4

Sample 2:

Sample size
`n_2` = 10

Sample mean
`\overline x_2` = 82.1

Standard deviation
`\sigma_2` = 12.0

To find the alternative hypothesis.

The null and alternative hypothesis can be computed as follows:

Null hypothesis:

`\mathbf{H_o = \sigma_1^2 = \sigma_2^2}`

Alternative hypothesis:

`\mathbf{H_a = \sigma_1^2 \\e \sigma_2^2}`

Since, alternative hypothesis is ≠, it shows that it is a two tailed test.