SOLUTION: **HELP* 12-2 What is the critical F-value when the sample size for the numerator is four and the sample size for the denominator is seven? Use a one-tailed test and the 0.01 signi

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Question 1202982: **HELP* 12-2
What is the critical F-value when the sample size for the numerator is four and the sample size for the denominator is seven? Use a one-tailed test and the 0.01 significance level. (Round your answer to 2 decimal places.)
Found 2 solutions by Theo, math_tutor2020:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Analysis of variance compares the means of a response variable for several groups. ANOVA compares the variation within each group to the variation of the mean of each group. The ratio of these two is the F statistic from an F distribution with (number of groups - 1) as the numerator degrees of freedom and (number of observations minus number of groups) as the denominator degrees of freedom.

the sample size of the groups is 4.
that would be the number of columns in the data set.
that says the number of groups is 4.
the degrees of freedom for the numerator is 4 minus 1 = 3

the sample size of the denominator is 7.
that would be the number of rows in the data set.
the total number of observations in the data set is 7 * 4 = 28

the degrees of freedom for the denominator is the number of total observations minus the number of groups = 28 minus 4 = 24

if this is right, the ceitical F at .01 level of significance would be the F for number of degrees of freedom for the numerator divided by the number of degrees of freedom for the denominator = F for column 3 intersect with row 24 = 4.718.

the critical F calculator gives the same resuls with greater precision as shown below.



a good reference to give you an idea of what's happening can be found at https://www.youtube.com/watch?v=-yQb_ZJnFXw




Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 9.78 (approximate)


Explanation:

n1 = sample size for the numerator = 4
n2 = sample size for the denominator = 7

df1 = degrees of freedom of the numerator
df1 = n1 - 1 = 4 - 1 = 3

df2 = degrees of freedom of the denominator
df2 = n2 - 1 = 7 - 1 = 6

Now turn to the appendix section of your stats textbook.
Look for the F distribution table.

If you don't have your textbook with you, then use something like this
http://socr.ucla.edu/Applets.dir/F_Table.html
or this
https://www.statology.org/f-distribution-table/
Many other such tables can be found online.

On either page, scroll down until reaching alpha = 0.01
Look at the column marked df1 = 3 and row df2 = 6
The value 9.780 is in this row and column combo.
This is the approximate critical F-value for these two degrees of freedom at this alpha level.

An alternative would be to use a calculator such as this
https://www.danielsoper.com/statcalc/calculator.aspx?id=4
Be sure to ask your professor if s/he allows the use of a calculator, or would prefer a table instead.


Further Reading
https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/04%3A_Inferences_about_the_Differences_of_Two_Populations/4.05%3A_F-Test_for_Comparing_Two_Population_Variances