Question

Consider the following sample information from Population A and Population B. Sample A Sample B n 24 16 s2 32 38 We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals a. .84. b. .67. c. 1.50. d. 1.19.

Answer 1

Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:

`F=(s^2_2)/(s^2_1)=(38)/(32)=1.19`

And the best option would be:

d. 1.19.

Explanation:

Data given and notation

`n_1 = 24` represent the sampe size 1

`n_2 =16` represent the sample size 2

`s^2_1 = 32` represent the sample variance for 1

`s^2_2 = 38` represent the sample variance for 2

The statistic for this case is given by:

`F=(s^2_1)/(s^2_2)`

Hypothesis to verify

We want to test if the true deviations are equal, so the system of hypothesis are:

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

H1:
`\sigma^2_1 \\eq \sigma^2_2`

Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:

`F=(s^2_2)/(s^2_1)=(38)/(32)=1.19`

And the best option would be:

d. 1.19.