Question

An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these records was selected for salespersons in each branch. All three branches are located in cities in which per capita income is the same. The executive wishes to compare these samples to see if there is a significant difference in performance of salespersons in the three different branches. If so, the information will be used to determine which of the managers to promote.

Branch Managed by Adams	Branch Managed by McDale	Branch Managed by Vasquez
7.8	8.6	6.3
6.6	10.9	8.1
10.7/	11.1	10.7
10.8	9.2	11.6
9.3
10.2

(b) Find

SS_TOT, SS_BET, and SS_W

and check that

SS_TOT = SS_BET + SS_W.

(Round your answers to three decimal places.)

SSTOT	=
SSBET	=
SSW	=

Find

d.f._BET, d.f._W, MS_BET, and MS_W.

(Round your answers to three decimal places.)

d.f.BET	=
d.f.W	=
MSBET	=
MSW	=

Find the value of the sample F statistic. (Round your answers to three decimal places.)


What are the degrees of freedom?
(numerator)=
(denominator)=

(f) Make a summary table for your ANOVA test. (Round your answers to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P-Value	Test Decision
Between groups					---Select--- P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.001 < P-value < 0.010 P-value < 0.001	---Select--- Do not reject H0. Reject H0.
Within groups
Total

Answer 1

	Adams	McDale	Vasquez	Total
Sum	55.4	39.8	36.7	131.9
Count	6	4	4	14
Mean, Sum/n	9.233333	9.95	9.175
Sum of square, Ʃ(xᵢ-x̅)²	14.53333	4.61	17.6275

b)

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 1.573

SS(within) = SS1 + SS2 + SS3 = 36.771

SS(total) = SS(between) + SS(within) = 38.344

Number of treatment, k = 3

Total sample Size, N = 14

df(between) = k-1 = 2

df(within) = N-k = 11

df(total) = N-1 = 13

MS(between) = SS(between)/df(between) = 0.786

MS(within) = SS(within)/df(within) = 3.343

F = MS(between)/MS(within) = 0.235

--

df(numerator) = 2

df(denominator) = 11

p-value = F.DIST.RT(0.2352, 2, 11) = 0.7943

--

ANOVA
Source of Variation	SS	df	MS	F	P-value	Test decision
Between Groups	1.573	2	0.786	0.235	P-value > 0.100	Do not reject
Within Groups	36.771	11	3.343
Total	38.344	13