Question

An adjunct instructor teaches the same statistics class at three different colleges. She wants to compare the average age of students in the three classes.

Random Sample of 10 Student Ages from Each College

School 1	25	23	23	21	19	17	20	21	31	29
School 2	26	21	23	24	19	22	19	24	28	31
School 3	24	23	22	22	20	19	22	23	30	28

(a)

Compute the grand mean.

(b)

Calculate the sum of squares treatment.

(c)

What is the sum of squares error?

(d)

What is the mean squares treatment?

(e)

What is the mean squares error? (Round your answer to four decimal places.)

(f)

Calculate the F statistic. (Round your answer to three decimal places.)

Answer 1

	School 1	School 2	School 3
	25	26	24
	23	21	23
	23	23	22
	21	24	22
	19	19	20
	17	22	19
	20	19	22
	21	24	23
	31	28	30
	29	31	28
Total(yi)	229	237	233
Averages y̅i	22.9	23.7	23.3
Treatment Effect	22.9 - 23.3 = -0.4	23.7 - 23.3 = 0.4	23.3 - 23.3 = 0

Overall total = 699
Overall mean µ = 699 / 30 = 23.3

y̅i .. is overall mean
y̅i. is treatment mean
SST = ΣΣ(Yij - Y̅..)²
SS treatment = ΣΣ(Yij - y̅i.)²
SS error = Σ(y̅i. - Y̅..)²

	Sum of Squares	Degree of freedom	Mean Square	F0 = MST / MSE	P value
Treatment	3.2	2	1.6	0.1061	0.8997
Error	407.1	27	15.0778
Total	410.3	29

Part a)

Overall mean µ = 699 / 30 = 23.3

Part b)

SS treatment = ΣΣ(Yij - y̅i.)²  = 3.2

Part c)

SS error = Σ(y̅i. - Y̅..)² = 407.1

Part d)

MS treatment = SS treatment / a-1 = 1.6

Part e)

MS error = SS error / N-a = 15.0778

Part f)

F0 = MST / MSE = 0.106