Question

model. A comprehensive statistics examination is given to 16 students in order to determine whether or not there is a significant difference in the performance of students majoring in the various disciplines of Business Administration. The following data show the scores of the 16 students (5 majoring in accounting, 6 majoring in management, and 5 majoring in marketing). Accounting 91 Management 63 92 86 Marketing 95 80 80 70 70 60 75 70 60 85 90 99

Answer 1

	Accounting	Management	Marketing	Total
Sum	386	485	395	1266
Count	5	6	5	16
Mean, Sum/n	77.2	80.83333	79
Sum of square, Ʃ(xᵢ-x̅)²	606.8	950.8333	820

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 16

df(between) = k-1 = 2

df(within) = N-k = 13

df(total) = N-1 = 15

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 36.1167

SS(within) = SS1 + SS2 + SS3 = 2377.6333

SS(total) = SS(between) + SS(within) = 2413.75

MS(between) = SS(between)/df(between) = 18.0583

MS(within) = SS(within)/df(within) = 182.8949

F = MS(between)/MS(within) = 0.0987

p-value = F.DIST.RT(0.0987, 2, 13) = 0.9067

Critical value Fc = F.INV.RT(0.05, 2, 13) = 3.80556525

Decision:

P-value > α, Do not reject the null hypothesis.

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	36.1167	2	18.0583	0.0987	0.9067
Within Groups	2377.6333	13	182.8949
Total	2413.7500	15

There is not enough evidence to conclude that there is a significant difference in the performance of the student in the three majors at 0.05 significance level.