M14 #19: An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these records was selected for salespersons in each branch. All three branches are located in cities in which per capita income is the same. The executive wishes to compare these samples to see if there is a significant difference in performance of salespersons in the three different branches. If so, the information will be used to determine which of the managers to promote.
| Branch Managed by Adams | Branch Managed by McDale | Branch Managed by Vasquez |
| 7.6 | 8.2 | 6.1 |
| 6.8 | 10.1 | 8.9 |
| 10.9 | 11.1 | 10.7 |
| 11.2 | 9.8 | 11.2 |
| 9.7 | ||
| 10.2 |
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.)
| Anova: Single Factor | ||||||
| SUMMARY | ||||||
| Groups | Count | Sum | Average | Variance | ||
| Adams | 6 | 56.4 | 9.4 | 3.244 | ||
| McDale | 4 | 39.2 | 9.8 | 1.446666667 | ||
| Vasquez | 4 | 36.9 | 9.225 | 5.315833333 | ||
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 0.704642857 | 2 | 0.352321429 | 0.106157248 | 0.900193 | 3.982298 |
| Within Groups | 36.5075 | 11 | 3.318863636 | |||
| Total | 37.21214286 | 13 | ||||
a)
SS tot= 37.212
SS bet = 0.705
SS within = 36.508
SSTOT = SSBET + SSW
as 37.2121 = 0.7046 + 36.5075
b)
d.f.BET = 2 , d.f.W = 11 ,
MSBET, = 0.3523 and MSW = 3.3189
c)
F = 0.1062
= 0.11
M14 #19: An executive at the home office of Big Rock Life Insurance is considering three...
M14 #19: An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these records was selected for salespersons in each branch. All three branches are located in cities in which per capita income is the same. The executive wishes to compare these samples...
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There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations. Site I Site II Site III 61 25 12 39 15 32 22 57 66 12 67 20 83 11 52 15 27 Shall we reject or not reject the claim that there...
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