Question 1207871: 1) A one-way ANOVA test is performed on three independent samples with n1 = 6, n2 = 7, and n3 = 8. What is the critical value obtained from the F-table for this test at the 2.5% level of significance?
a) 39.45
b) 4.56
c) 3.55
d) 29.45
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
k = 3 groups
N = n1+n2+n3 = 6+7+8 = 21
df = degrees of freedom
df1 = k-1 = 3-1 = 2
df2 = N-k = 21-3 = 18
You mention using an F-table, but didn't provide the actual table.
I'll assume it looks like something found at this link
http://socr.ucla.edu/Applets.dir/F_Table.html
I'll be using the table that has the title "alpha = 0.025" at the top of the table.
Highlight the column labeled df1 = 2 at the top
Highlight the row labeled df2 = 18 at the left side
This row and column intersect to yield the approximate value 4.5597 which rounds to 4.56
Therefore the answer is option B
Caution: The order of df1 and df2 is important. Swapping them will yield the wrong critical value.
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Another approach is to use a calculator such as this
https://www.danielsoper.com/statcalc/calculator.aspx?id=4
Want to use a TI83 or TI84?
Unfortunately there isn't an inverseF function (similar how there's invNorm), but you can follow the process mentioned in this video
https://www.youtube.com/watch?v=Bes5pTe3C6I
Want to use a spreadsheet?
You can use a function called finv
The template would be
=finv(area,df1,df2)
So in your case you would type in
=finv(0.025,2,18)
Don't forget about the equal sign up front.
Check out this page for the documentation of the finv function
https://support.microsoft.com/en-us/office/finv-function-4d46c97c-c368-4852-bc15-41e8e31140b1
Further Reading
https://www.statology.org/one-way-anova/
https://www.itl.nist.gov/div898/handbook/prc/section4/prc433.htm
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