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).IIIIIIIV27.213.322.217.323.29.320.116.614.811.87.914.48.28.712.215.111.36.57.710.2 19.7 9.8Shall 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 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= (c) Find the value of the sample F statistic. (Use 3 decimal places.)(d) Make a summary table for your ANOVA test.

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Asked Dec 16, 2019
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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
27.2 13.3 22.2 17.3
23.2 9.3 20.1 16.6
14.8 11.8 7.9 14.4
8.2 8.7 12.2 15.1
11.3 6.5 7.7 10.2
  19.7   9.8

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


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

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

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Expert Answer

Step 1

Given data and calculation is shown below

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II Ш IV 27.2 13.3 22.2 17.3 23.2 9.3 20.1 16.6 14.8 7.9 11.8 14.4 15.1 8.2 8.7 12.2 11.3 6.5 7.7 10.2 19.7 9.8 Sum =84.7 Sum = 69.3 Sum = 70.1 Sum = 83.4 Mean Mean = Mean = %3D 16.94 11.55 14.02 Mean = 13.9 Std dev Std dev = Std dev = Std dev = = 8.019 4.653 6.793 3.195 Grand mean is given by 5 x 16.94 + 6 × 11.55 + 5 × 14.02 + 6 × 13.9 I = 13.977 5+6+5+ 6

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Step 2

SSBetween is given by

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SSBetween = E=1n;(X¡ – X)² = 5 × (16.94 – 13.977)² + 6 × (11.55 – 13.977)² + 5 x (14.02 – 13.977)² + 6 x (13.9 – 13.977)2 = 79.284 d.o.fßetween = 4-1= 3 SSBetween 79.284 MSBetween = 26, 428 d.o. fBetween 3 (п, — 1) x s? SSwithin i=1 (5 – 1) × 8.019² + (6 – 1) × 4.6532 + (5 – 1) × 6.7932 + (6 – 1) × 3.1952 601.089 d.o.fwithin = 21 – 3= 18 SSwithin 601.089 MSwithin = 33.394 d.o.fwithin 18

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Step 3

Test-statistic is...

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MSBetween MSwithin 26.428 0.791 33.395 Considering significance level a = 0.05 Critical value of F is given by Fafbetween.df within.0.05 F3,18,0.05 = 3. 15991(From Excel = F.INV.RT(0.05,3,18))

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