Question

In: Statistics and Probability

M14 #15: How productive are U.S. workers? One way to answer this question is to study...

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

B) Find d.f.BET, d.f.W, MSBET, and MSW. (Use 4 decimal places for MSBET, and MSW.)

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

Solutions

Expert Solution

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:

-------------

Now

C)

F test statistics is

------------

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.


Related Solutions

#15 How productive are U.S. workers? One way to answer this question is to study annual...
#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 13.2 22.7 17.9 23.4 9.2 20.4 16.9 14.3 11.5 7.2 14.8 8.4 8.2 12.7 15.1 11.8 6.5 7.0 10.2 19.8 9.8 (b) Find SSTOT, SSBET, and...
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 27.2 13.3 22.9 17.2 23.3 9.8 20.2 16.6 14.4 11.7 7.8 14.1 8.7 8.2 12.2 15.9 11.5 6.3 7.9 10.1 19.3 9.4 Shall we reject or not reject...
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 27.9 13.2 22.2 17.2 23.1 9.7 20.3 16.2 14.3 11.6 7.6 14.9 8.6 8.4 12.1 15.3 11.2 6.3 7.3 10.6 19.4 9.2 Shall we reject or not reject...
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 27.5   13.6   22.6   17.2 23.7   9.6   20.5   16.5 14.6   11.4   7.3   14.2 8.1   8.2   12.9   15.9 11.6   6.8   7.7   10.5 19.9       9.1 Shall we reject or not...
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 27.2 13.2 22.8 17.8 23.4 9.6 20.1 16.2 14.6 11.7 7.4 14.1 8.9 8.1 12.3 15.4 11.9 6.9 7.0 10.8 19.6 9.6 Shall we reject or not reject...
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 13.9 22.7 17.8 23.9 9.4 20.5 16.6 14.4 11.5 7.1 14.2 8.1 8.7 12.9 15.4 11.2 6.8 7.7 10.2 19.2 9.5 Shall we reject or not reject...
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 27.5 13.7 22.8 17.1 23.3 9.3 20.3 16.7 14.7 11.7 7.9 14.5 8.6 8.9 12.5 15.3 11.5 6.1 7.2 10.4 19.2 9.1 Shall we reject or not reject...
How productive are employees? One way to answer this question is to study annual company profits...
How productive are employees? One way to answer this question is to study annual company profits per employee. Let x1 represent annual profits per employee in computer stores in St. Louis. A random sample of n1 = 11 computer stores gave a sample mean of x1 = $25,200 profit per employee with sample standard deviation s1 = $8,400. Another random sample of n2 = 9 building supply stores in St. Louis gave a sample mean x2 = $19,900 per employee...
How profitable are different sectors of the stock market? One way to answer such a question...
How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 28 retail stocks such as Toys 'R' Us, Best Buy, and Gap was studied for x1, profit as a percentage of stockholder equity. The result was x1 = 13.9. A random sample of 36 utility (gas and electric) stocks such as Boston Edison, Wisconsin Energy, and Texas Utilities was studied...
How profitable are different sectors of the stock market? One way to answer such a question...
How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 25 retail stocks such as Toys 'R' Us, Best Buy, and Gap was studied for x1, profit as a percentage of stockholder equity. The result was x1 = 14.8. A random sample of 30 utility (gas and electric) stocks such as Boston Edison, Wisconsin Energy, and Texas Utilities was studied...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT