#16
A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars).
| I | II | III |
| 49.5 | 55.1 | 39.1 |
| 43.5 | 25.3 | 37.2 |
| 32.9 | 41.1 | 10.9 |
| 27.9 | 29.5 | 32.6 |
| 38.1 | 39.4 | 15.5 |
| 36.2 | 42.6 | |
| 20.7 |
Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the three types of companies? Use a 1% 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 | NA | NA. | ||||
| Within groups | ||||||
| Total |
| I | II | III | ||||
| count, ni = | 7 | 5 | 6 | |||
| mean , x̅ i = | 35.543 | 38.08 | 29.65 | |||
| std. dev., si = | 9.581 | 11.592 | 13.225 | |||
| sample variances, si^2 = | 91.800 | 134.372 | 174.899 | |||
| total sum | 248.8 | 190.4 | 177.9 | 617.1 | (grand sum) | |
| grand mean , x̅̅ = | Σni*x̅i/Σni = | 34.28 | ||||
| square of deviation of sample mean from grand mean,( x̅ - x̅̅)² | 1.586 | 14.415 | 21.468 | |||
| TOTAL | ||||||
| SS(between)= SSB = Σn( x̅ - x̅̅)² = | 11.105 | 72.073 | 128.807 | 211.9849 | ||
| SS(within ) = SSW = Σ(n-1)s² = | 550.797 | 537.488 | 874.495 | 1962.780 | ||
no. of treatment , k = 3
df between = k-1 = 2
N = Σn = 18
df within = N-k = 15
mean square between groups , MSB = SSB/k-1 =
105.9924
mean square within groups , MSW = SSW/N-k =
130.8520
F-stat = MSB/MSW = 0.8100
P value = 0.4634
-------------------
Ho: µ1=µ2=µ3
H1: not all means are equal
---------
| SSTOT | = | 2174.765 |
| SSBET | = | 211.985 |
| SSW | = | 1962.780 |
| dfBET | = | 2 |
| dfW | = | 15 |
| MSBET | = | 105.992 |
| MSW | = | 130.852 |
value of the sample F statistic=0.810
the degrees of freedom?
(numerator)=2
(denominator)=15
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | test decision |
| Between Groups | 211.985 | 2 | 105.992 | 0.810 | 0.463 | do not reject Ho |
| Within Groups | 1962.780 | 15 | 130.852 | |||
| Total | 2174.765 | 17 |
#16 A random sample of companies in electric utilities (I), financial services (II), and food processing...
A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars). I II III 49.7 55.3 39.0 43.4 25.0 37.9 32.4 41.7 10.7 27.2 29.8 32.8 38.7 39.5 15.6 36.6 42.4 20.8 (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...
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