Question

A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars).

I	II	III
49.4	55.3	38.7
43.7	24.7	37.7
32.6	41.3	10.7
27.5	29.8	32.8
38.1	39.1	15.5
36.7		42.1
20.8

Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the three types of companies? Use a 1% level of significance.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

SSTOT	=
SSBET	=
SSW	=

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

dfBET	=
dfW	=
MSBET	=
MSW	=

Find the value of the sample F statistic. (Use 3 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

(f) Make a summary table for your ANOVA test.

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

Appplying regression:

b)

SSTOT	=	2,197.765
SSBET	=	214.188
SSW	=	1,983.577

dfBET	=	2
dfW	=	15
MSBET	=	107.094
MSW	=	132.238

value of the sample F statistic =0.810

degrees of freedom (numerator)=2

degrees of freedom (Denominator)=15

c) P-value > 0.100

f)

Source of Variation	SS	df	MS	F	P-value	test decision
Between Groups	214.188	2	107.094	0.810	0.4635	Do not reject Ho
Within Groups	1983.577	15	132.238
Total	2197.765	17