n 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.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 |
| 7.8 | 8.8 | 6.5 |
| 6.6 | 10.3 | 8.7 |
| 10.1 | 11.7 | 10.1 |
| 10.6 | 9.4 | 11.4 |
| 9.1 | ||
| 10.2 |
Use a 1% level of significance. Shall we reject or not reject the claim that there are no differences among the performances of the salespersons in the different branches?
(b) Find
and check that
(Round your answers to three decimal places.)
|
SSTOT
|
= | |
|
SSBET
|
= | |
|
SSW
|
= |
Find
(Round your answers to three decimal places.)
|
d.f.BET
|
= | |
|
d.f.W
|
= | |
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MSBET
|
= | |
|
MSW
|
= |
Find the value of the sample F statistic. (Round your answers to three decimal places.)
What are the degrees of freedom?
(numerator)
(denominator)
(f) Make a summary table for your ANOVA test. (Round your answers to three decimal places.)
| Source of Variation |
Sum of Squares |
Degrees of Freedom |
MS | F Ratio |
||
| Between groups | ||||||
| Within groups | ||||||
| Total |
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