Question

Scott is curious as to whether or not the students at three different schools are equally smart. He collects a sample of 9 students from Wilson High School, 9 students from Lakewood HS, 9 from Millikan HS and give same tests. The average for Wilson was 75, Lakewood was 77, Millikan was 88. (The average for all 27 students was 80) The SS(Within)=1920. Calculate F-Stat

What I have so far:

F = (882/2) / (1920/24) = 5.5125 > 3.40 (Critical Value) , therefore, reject Null.

However, I do not understand how to obtain denominator of 1920, which is 24. I need help on how to obtain number 24 above.

Answer 1

Scott is curious as to whether or not the students at three different schools are equally smart. He collects a sample of 9 students from Wilson High School, 9 students from Lakewood HS, 9 from Millikan HS and give same tests. The average for Wilson was 75, Lakewood was 77, Millikan was 88. (The average for all 27 students was 80)The SS(Within) = 1920. Calculate F-State SS_Between = SS_B = n_1 (x_1 -x)^2 + n_2 (x_2 -x)^2 + n_3(x_3 -x)^2 = 9(75-80)^2 + 9)77-80)^2 + 9(88-80)^2 = 9(25 + 9 + 64) = 9(98) = 882