What is the critical value of f for a one-tailed test at the α =.10 level, when there is a sample size of 8 for the sample with the smaller variance and a sample size of 11 for the sample with the larger sample variance?

a. 3.64
b. 2.70
c. 2.41
d. 1.65

b. 2.70

Step-by-step explanation:

Data given and notation  

represent the sampe size for sample 1

represent the sample size for sample 2

represent the sample deviation for sample 1

represent the sample variance for sample 1

represent the sample deviation for sample 2

represent the sample variance for sample 2

represent the significance level provided

Confidence =0.90 or 90%

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:

System of hypothesis

We want to test for example if the variation for group 1 it's higher than the variation for group 2, so the system of hypothesis are:

H0:

H1:

Calculate the statistic

Now we can calculate the statistic like this:

Calculate the critical value

Now we can calculate the critical value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have and for the denominator we have and the F statistic have 10 degrees of freedom for the numerator and 7 for the denominator. And the critical value would be:

And we can find it with the following excel code: "=F.INV(0.9,10,7)"

b. 2.70

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