The F-test for equal population variances is carried out on two independent samples containing n1 = 9 and n2 = 8 observational units in each sample. If the significance level (α) for this 2-tailed test is 0.05, what is the corresponding critical value (F*)? Assume that the variance for group 1 is larger than the variance for group 2.3.394.364.93.73
Question
The F-test for equal population variances is carried out on two independent samples containing n1 = 9 and n2 = 8 observational units in each sample. If the significance level (α) for this 2-tailed test is 0.05, what is the corresponding critical value (F*)? Assume that the variance for group 1 is larger than the variance for group 2.3.394.364.93.73
Solution
To find the critical value (F*) for an F-test, we need to refer to the F-distribution table. The degrees of freedom for the numerator (df1) and the denominator (df2) are determined by the sample sizes of the two groups.
In this case, df1 = n1 - 1 = 9 - 1 = 8 and df2 = n2 - 1 = 8 - 1 = 7.
The significance level (α) for a 2-tailed test is 0.05. However, F-distribution tables typically provide critical values for a one-tailed test. Therefore, we need to adjust the significance level for a one-tailed test, which is 0.025 in each tail (0.05/2).
Now, we look up the critical value in the F-distribution table with df1 = 8 and df2 = 7 at the 0.025 significance level.
Please note that the exact value might slightly differ depending on the specific F-distribution table used. However, based on a commonly used table, the critical value (F*) is approximately 3.73.
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