Midterm ANOVA question

a) Here is the table:

Source	Df	SS	MS	F
Factor	2	15,753,673.17	7,876,836.585	11.26
Error	9	6,296,223.75	699,580.4167
Total	11	22,049,896.92

b) Ho: s1 = s2 = s3

Ha: Not all standard deviations equal

Reject Ho if H > 27.8

H = 1,399,688.333/264,164.9197 = 5.299

Do not reject Ho

Conclude no significant difference in variances.

c) Ho: µ1 = µ2 = µ3

Ha: Not all means equal

Reject Ho if F > 4.26

F = 11.26 (from ANOVA table)

Reject Ho.

Conclude there is a significant difference in the mean amounts spent by the groups.

d) P-value = P(F > 11.26). The 1% critical value is 8.02. Therefore, the p-value < 1% and, by extension, the 5% level of significance and we reject Ho.

e) D = 3.95sqrt(699,580.4167/4) = 1,651.91

Male/Female

(6,095 – 4,211.75) ± 1,651.91

231.34 < µ1 - µ2 < 3.535.16

Conclude µ1 ≠ µ2

Male/Married

(6955.5 - 6,095) ± 1,651.91

-791.41 < µ3 - µ1 < 2,512.41

Conclude µ1 = µ3

Female/Married

(6,955.5 – 4,211.75) ± 1,651.91

1,091.84 < µ3 - µ2 < 4,395.66

Conclude µ2 ≠ µ3

Looking at all 3 intervals together, we can conclude that not all population means are equal which support the conclusion in ANOVA to reject Ho.