the numerator in the f-test is the sample that has the greatest variation.
i don't see variations here, so that's a problem for you to find.
since we are dealing with a two tail test, then we have to take half of the significance level, making it equal to .01
that's the significance level to use for the f-test.
we'll make some assumption since we don't know who has the greatest variation.
if we assume sample 1 has the greatest variation, then sample 1 is the numerator ande sample 2 is the denominator and the critical f-value will be found with sample 1 degrees of freedom in the numerator and sample 2 degrees of freedom in the denominator.
degrees of freedom is sample size minus 1.
therefore dof sample 1 = 16 minus 1 = 15 and doc sample 2 = dof sample 2 = 10 minus 1 = 9.
the critical f-value will be f(15/9) = 4.96207836
here's what that looks like in the calcuator found at https://www.danielsoper.com/statcalc/calculator.aspx?id=4
if we assume sample 2 has the greatest variation, then sample 2 is the numerator and sample 1 is the denominator and the critical f-value will be found with sample 2 degrees of freedom in the numerator and sample 1 degrees of freedom in the denominator.
since degrees of freedom = sample size minus 1, then dof sample 1 = 16 minus 1 = 15 and dof sample 2 = 10 minus 1 = 9.
the critical f-value will be f(9/15)) = 3.89478811.
here's what that looks like in the calcuator found at https://www.danielsoper.com/statcalc/calculator.aspx?id=4
here's the reference that i used to help me answer this question.
https://www.youtube.com/watch?v=MLhSGiAxhVk&list=RDCMUCs3IhN8VOA_5WxpAgbSmFkg&index=2
she use the critical f-test valueu table rather than the calculator that i used.
the table is found at http://www.socr.ucla.edu/Applets.dir/F_Table.html
here's the part of the table that deals with .01 significance level.
the values in the table for 15/9 and 9/15 agree with the calculator results.
the numerator is the column number and the denominator is the number.
f(15/9) is in column 15 row 9
f(9/15) is in column 9 row 15
i'm pretty sure this is correct after looking at the refeence.
i am, however, still learning about f-test and anovas, so keep that in mind when looking at the solution.
my instructor has been the videos on youtube.com
the ones by brandon foltz and david longstreet and professor essa have been phelpful for me.
thee are others on youtube as well that i haven't gone through.