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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