Question

How productive are U.S. workers? One way to answer this question is to study annual profits...

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 13.5 22.2 17.5
23.8 9.8 20.3 16.9
14.9 11.9 7.9 14.7
8.4 8.8 12.4 15.3
11.4 6.1 7.4 10.5
19.8 9.2

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.

(a) What is the level of significance?

(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)

SSTOT =
SSBET =
SSW =


Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)

dfBET =
dfW =
MSBET =
MSW =


Find the value of the sample F statistic. (Use 3 decimal places.)


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

(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
Within groups
Total

Homework Answers

Answer #1

applying one way ANOVA on above data:

a) level of significance=0.05

b)

SSTOT=705.458

SSBET=82.891

SSW=622.567

dfBET=3

dfW=18

MSBET=82.891/3=27.630

MSW=622.567/18=34.587

value of the sample F statistic =MSBET/MSE=27.630/34.587=0.799

degrees of freedom (numerator)=3

degrees of freedom (denominator)=18

Source of variation SS df MS F p vlaue Decision
treatments 82.891 3.00 27.630 0.799 0.5105 Do not reject Ho
error 622.567 18.00 34.587
total 705.458 21.00
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