Question

M14 #15: 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	13.8	22.6	17.9
23.6	9.7	20.4	16.6
14.8	11.8	7.5	14.2
8.1	8.9	12.3	15.2
11.1	6.8	7.4	10.7
	19.1		9.9

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

B) Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 4 decimal places for MS_BET, and MS_W.)

C) Find the value of the sample F statistic. (Use 2 decimal places.)

Answer 1

Following table shows the calculations:

	G1, I	G2, II	G3, III	G4, IV
	27.3	13.8	22.6	17.9
	23.6	9.7	20.4	16.6
	14.8	11.8	7.5	14.2
	8.1	8.9	12.3	15.2
	11.1	6.8	7.4	10.7
		19.1		9.9
Total	84.9	70.1	70.2	84.5

Following table shows the calculations:

	G	G^2
	27.3	745.29
	23.6	556.96
	14.8	219.04
	8.1	65.61
	11.1	123.21
	13.8	190.44
	9.7	94.09
	11.8	139.24
	8.9	79.21
	6.8	46.24
	19.1	364.81
	22.6	510.76
	20.4	416.16
	7.5	56.25
	12.3	151.29
	7.4	54.76
	17.9	320.41
	16.6	275.56
	14.2	201.64
	15.2	231.04
	10.7	114.49
	9.9	98.01
Total	309.7	5054.51

So we have

A)

Now,

B)

Since there are 4 different groups so we have k=4. Therefore degree of freedoms are:

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Now

C)

F test statistics is

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So p-value of the test is 0.5405. Since P-value is not less than 0.05 so we cannot conclude that populations mean are different.