Question

How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars).

I	II	III	IV
27.3	13.7	22.5	17.8
23.6	9.4	20.1	16.4
14.9	11.6	7.7	14.2
8.9	8.6	12.4	15.6
11.8	6.6	7.2	10.7
	19.2		9.6

Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% 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)

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

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

Applying ANOVA on above data:

b)

SSTOT	=	689.533
SSBET	=	91.321
SSW	=	598.211

dfBET	=	3
dfW	=	18
MSBET	=	30.440
MSW	=	33.234

value of the sample F statistic =0.916

degrees of freedom (numerator)=3

degrees of freedom (Denominator)=18

P-value > 0.100

Source of Variation	SS	df	MS	F	P-value	Decision
Between Groups	91.321	3	30.440	0.916	0.4530	Do not reject
Within Groups	598.211	18	33.234
Total	689.533	21