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
7.4	8.6	6.9
6.6	10.9	8.3
10.3	11.3	10.5
11.2	9.6	11.8
9.7
10.2

Use a 1% level of significance. Shall we reject or not reject the claim that there are no differences among the performances of the salespersons in the different branches?

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: μ₁ = μ₂ = μ₃; H₁: Not all the means are equal.H_o: μ₁ = μ₂ = μ₃; H₁: All three means are different.    H_o: μ₁ = μ₂ = μ₃; H₁: At least two means are equal.H_o: μ₁ = μ₂ = μ₃; H₁: Exactly two means are equal.

(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)

(c) Find the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P value is greater than the level of significance at α = 0.01, we do not reject H₀.Since the P value is less than or equal to the level of significance at α = 0.01, we reject H₀.    Since the P value is greater than the level of significance at α = 0.01, we reject H₀.Since the P value is less than or equal to the level of significance at α = 0.01, we do not reject H₀.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal.    At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal.

(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
Within groups
Total

Answer 1

a)

level of significance =0.01

Ho: μ1 = μ2 = μ3; H1: Not all the means are equal

b)

SSTOT	37.384
SSBET	1.923
SSW	35.461

dfBET	2
dfW	11
MSBET	0.961
MSW	3.224

value of test statistic for factor A =

0.298

df(numerator) =		2
df(Denominator) =		11

c)

P-value > 0.100

d)

Since the P value is greater than the level of significance at α = 0.01, we do not reject H0.

e_)

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.

f_)

Source	SS	df	MS	F	P value	decision
Between	1.923	2	0.961	0.298	0.7480	fail to reject Ho
Within	35.461	11	3.224
Total	37.384	13