Question

If testing the claim that sigma subscript 1 superscript 2 baseline not equals sigma subscript 2 superscript 2σ21≠σ22​, what do we know about the two samples if the test statistic is fequals=​1?

Answer 1

Answer:

The statistic for this system of hypothesis is given by:

$F=\frac{s^2_1}{s^2_2}$

If the statistic is equal to 1 then that means $s^2_1 = s^2_2$ and we don't have enough evidence to conclude that the two population variances and deviations are different.

Step-by-step explanation:

System of hypothesis

We want to test if the variation for a group1 is equal to another one 2, so the system of hypothesis are:

H0: $\sigma^2_1 = \sigma^2_2$

H1: $\sigma^2_1 \neq \sigma^2_2$

Calculate the statistic

The statistic for this system of hypothesis is given by:

$F=\frac{s^2_1}{s^2_2}$

If the statistic is equal to 1 then that means $s^2_1 = s^2_2$ and we don't have enough evidence to conclude that the two population variances and deviations are different.