Question

What is the critical f value for a sample of six observations in the numerator and four in the denominator? use a two-tailed test and the 0.10 significance level

Answer 1

"=F.INV(0.025,5,3)"
`F_(\alpha/2)= 0.128`

"=F.INV(1-0.025,5,3)"
`F_(1-\alpha/2)=14.885`

Explanation:

Previous concepts

F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:

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

Where
`s^2_1 > s^2_2`. On this case we need to find the degrees of freedom for the numerator and denominator like this:

`df_(num)= n-1= 6-1= 5`

`df_(den)= n-1=4-1= 3`

Now for the critical value we are using a two tailed test so then we need to look on the F distribution with 5 degrees of freedom on the numerator and 3 on the denominator one critical value that accumulates 0.05 of the ara on the left tail and 0.05 of the area on the right tail. We can use the following excel codes:

"=F.INV(0.025,5,3)"
`F_(\alpha/2)= 0.128`

"=F.INV(1-0.025,5,3)"
`F_(1-\alpha/2)=14.885`

And we have our critical values on this case.

Answer 2

The critical f value of a sample of six observations in the numerator and four in the denominator can be determined by using F Tables. There are given F tables in statistics books for reference. Find the table for significance level of 10% or 0.10 and two-tailed. Locate from the table, numerator of 6 and denominator of 4. The critical f value is 4.010.