Question
In: Statistics and Probability
#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 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 | NA | NA | ||||
| Within groups | ||||||
| Total |
Solutions
Expert Solution
One Way Analysis of Variance (ANOVA)
| I | II | III | IV | |||
| count, ni = | 5 | 6 | 5 | 6 | ||
| mean , x̅ i = | 17.040 | 11.40 | 14.00 | 14.12 | ||
| std. dev., si = | 7.990 | 4.752 | 7.307 | 3.39 | ||
| sample variances, si^2 = | 63.833 | 22.580 | 53.395 | 11.494 | ||
| total sum | 85.2 | 68.4 | 70 | 84.7 | 308.3 | (grand sum) |
| grand mean , x̅̅ = | Σni*x̅i/Σni = | 14.01 | ||||
| square of deviation of sample mean from grand mean,( x̅ - x̅̅)² | 9.159 | 6.831 | 0.000 | 0.011 | ||
| TOTAL | ||||||
| SS(between)= SSB = Σn( x̅ - x̅̅)² = | 45.794 | 40.987 | 0.001 | 0.064 | 86.84558 | |
| SS(within ) = SSW = Σ(n-1)s² = | 255.332 | 112.900 | 213.580 | 57.468 | 639.280 | |
no. of treatment , k = 4
df between = k-1 = 3
N = Σn = 22
df within = N-k = 18
mean square between groups , MSB = SSB/k-1 =
28.9485
mean square within groups , MSW = SSW/N-k =
35.5156
F-stat = MSB/MSW = 0.8151
P value = 0.5022
---------------
| SSTOT | = | 726.126 |
| SSBET | = | 86.8 |
| SSW | = | 639.280 |
| dfBET | = | 3 |
| dfW | = | 18 |
| MSBET | = | 28.949 |
| MSW | = | 35.516 |
value of the sample F statistic=0.815
(numerator) DF=3
(denominator) DF = 18
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | test decision |
| Between Groups | 86.846 | 3 | 28.949 | 0.815 | >0.10 | do not reject Ho |
| Within Groups | 639.280 | 18 | 35.516 | |||
| Total | 726.126 | 21 |
orchestra answered 1 year agoRelated Solutions
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...
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...
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