Answer all the following questions as soons as possible ( not in excel format) W

Question

Answer all the following questions as soons as possible ( not in excel format)

What is the mean of sales for City 1 (Oil Change)? What is the mean of sales for City 2 (Tune-Up)? What is the SSA (Sum of Squares between groups/between group variance)? What is the MSA (Mean Sum of Squares between groups)? hat is the SSE (Sum of Squares within groups/within group variance)? What is the MSE (Mean Sum of Squares within groups)? What is the critical value for the F test when a=.05? hypothesis when a=.05?

Explanation / Answer

1) mean(City 1), x1 = (15+15+10+10+15+45+40+30+20+20)/10 = 22

2) mean(City 2), x2 = (30+25+45+20+25+25+30+40+30+30)/10 = 30

3) Grand mean, X = (15+15+10+10+15+45+40+30+20+20+30+25+45+20+25+25+30+40+30+30)/20 = 520/20 = 26
SSA = n*(xi - X)2 = 5*[(22-26)2 + (30-26)2] = 5*[16+16] = 160     (n is the number of observation in each group)

4) Degree of freedom for between groups, DFA = 2-1 = 1     (no. of groups - 1)
MSA = SSA/DFA = 160/1 = 160

5) MSE = (xi - xi)2

SSE = 1360 + 500 = 1860

6) DFE = 20-2 = 18 (no. of observations - no. of groups)
MSE = SSE/DFE = 1860/18 = 103.33

7) For = 0.05, DF = (1,18), Fcrit = 4.4139

H0 : m1 = m2 ;HA: Atleast one of the means is different from the others
F = MSA/MSE = 160/103.33 = 1.5484 < 4.4139
p = 0.2293 < 0.05
Fail to reject H0 and there is no sufficient evidence to suggest atleast one of the means is different from the others.

Data City 1(Oil Change) (City1 - mean(City1))2 City 2(Tune-up) (City2 - mean(City2))2 Store 1 15 49 30 0 Store 2 15 49 25 25 Store 3 10 144 45 225 Store 4 10 144 20 100 Store 5 15 49 25 25 Store 6 45 529 25 25 Store 7 40 324 30 0 Store 8 30 64 40 100 Store 9 20 4 30 0 Store 10 20 4 30 0 Total 220 1360 300 500 Mean 22 30

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