A marketing organization wishes to study the effects of four sales methods on we
ID: 3366697 • Letter: A
Question
A marketing organization wishes to study the effects of four sales methods on weekly sales of a product. The organization employs a randomized block design in which three salesman use each sales method. The results obtained are given in the following table, along with the Excel output of a randomized block ANOVA of these data.
(a) Test the null hypothesis H0 that no differences exist between the effects of the sales methods (treatments) on mean weekly sales. Set ? = .05. Can we conclude that the different sales methods have different effects on mean weekly sales?
F = 9.25, p-value = .0114; (Click to select)Do not rejectReject H0: there is (Click to select)no differencea difference in effects of the sales methods (treatments) on mean weekly sales.
(b) Test the null hypothesis H0 that no differences exist between the effects of the salesmen (blocks) on mean weekly sales. Set ? = .05. Can we conclude that the different salesmen have different effects on mean weekly sales?
F = 33.36, p-value = .0006; (Click to select)RejectDo not reject H0: salesman (Click to select)dodo not have an effect on sales
(c) Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the sales method effects on mean weekly sales. Which sales method(s) maximize mean weekly sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)
Salesman, j Sales Method, i A B C 1 36 32 25 2 41 31 26 3 33 23 19 4 35 20 13Explanation / Answer
Result:
(a) Test the null hypothesis H0 that no differences exist between the effects of the sales methods (treatments) on mean weekly sales. Set ? = .05. Can we conclude that the different sales methods have different effects on mean weekly sales?
F = 9.25, p-value = .0114; (Reject H0: there is a difference in effects of the sales methods (treatments) on mean weekly sales.
(b) Test the null hypothesis H0 that no differences exist between the effects of the salesmen (blocks) on mean weekly sales. Set ? = .05. Can we conclude that the different salesmen have different effects on mean weekly sales?
F = 33.36, p-value = .0006; Reject H0: salesman do have an effect on sales
(c) Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the sales method effects on mean weekly sales. Which sales method(s) maximize mean weekly sales?
(c) Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the sales method effects on mean weekly sales. Which sales method(s) maximize mean weekly sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)
Method 1 – Method 2:
[-9.34,6.01 ]
Method 1 – Method 3:
[-1.68, 13.68 ]
Method 1 – Method 4:
[0.66, 16.01 ]
Method 2 – Method 3:
[-0.01, 15.34 ]
Method 2 – Method 4:
[2.32, 17.68 ]
Method 3 – Method 4:
[-5.34,10.01 ]
MINITAB used.
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Method
3
204.33
68.111
9.25
0.011
salesman
2
491.17
245.583
33.36
0.001
Error
6
44.17
7.361
Total
11
739.67
Tukey Simultaneous Tests for Differences of Means
Difference
of Method
Levels
Difference
of Means
SE of
Difference
Simultaneous
95% CI
T-Value
Adjusted
P-Value
2 - 1
1.67
2.22
(-6.01, 9.34)
0.75
0.873
3 - 1
-6.00
2.22
(-13.68, 1.68)
-2.71
0.122
4 - 1
-8.33
2.22
(-16.01, -0.66)
-3.76
0.036
3 - 2
-7.67
2.22
(-15.34, 0.01)
-3.46
0.050
4 - 2
-10.00
2.22
(-17.68, -2.32)
-4.51
0.016
4 - 3
-2.33
2.22
(-10.01, 5.34)
-1.05
0.727
Individual confidence level = 98.66%
Method 1 – Method 2:
[-9.34,6.01 ]
Method 1 – Method 3:
[-1.68, 13.68 ]
Method 1 – Method 4:
[0.66, 16.01 ]
Method 2 – Method 3:
[-0.01, 15.34 ]
Method 2 – Method 4:
[2.32, 17.68 ]
Method 3 – Method 4:
[-5.34,10.01 ]
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