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

Answer:

Alternative hypothesis:

$\mathbf{H_a = \sigma_1^2 \ne \sigma_2^2}$

Step-by-step 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:

$\mathbf{H_a = \sigma_1^2 \ne \sigma_2^2}$

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