(c) Use Tukey simultaneous 95 percent confidence intervals to make pairwise comp

Question

(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:

Method 1 - Method 3:

Method 1 - Method 4:

Method 2 - Method 3:

Method 2 - Method 4:

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. Salesman Sales Method, i 37 43 31 29 29 23 23 27 16 14 ANOVA: Two-Factor without Replication SUMMARY Count Sum Average Method 1 Method 2 Method 3 Method 4 Salesman A Salesman B Salesman C Variance 49.3333 76.0000 8929.6667 99 33.0000 70 23.3333 56.3333 71 23.6667 112.3333 4 146 4 103 36.50 25.75 20.00 25.0000 14.2500 36.6667 ANOVA Source of Variation MS 66.9722 280.5833 df P-Value 0034 0001 F crit 4.7571 5.1433 200.9167 561.1667 26.8333 788.9167 14.98 62.74 Columns 4.47222 Total

Explanation / Answer

Here I write Given Table as like below in Minitab;

Then Go to option "Stat" then go to "ANOVA" then go to "General linear model"

and Then choose respective options. For tuckey test additionally go to "Comparism" potion and choose Tuckey

test and click ok.

Then we get Following output as ;

Factor Type Levels Values
Method fixed 4 1, 2, 3, 4
Salesman fixed 3 1, 2, 3

Analysis of Variance for Y, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Method 3 200.92 200.92 66.97 14.98 0.003
Salesman 2 561.17 561.17 280.58 62.74 0.000
Error 6 26.83 26.83 4.47
Total 11 788.92

S = 2.11476 R-Sq = 96.60% R-Sq(adj) = 93.76%

Grouping Information Using Tukey Method and 95.0% Confidence

Method N Mean Grouping
2 3 33.00 A
1 3 29.67 A
4 3 23.67 B
3 3 23.33 B

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests
Response Variable Y
All Pairwise Comparisons among Levels of Method
Method = 1 subtracted from:

Difference SE of Adjusted
Method of Means Difference T-Value P-Value
2 3.333 1.727 1.930 0.3088
3 -6.333 1.727 -3.668 0.0395
4 -6.000 1.727 -3.475 0.0493

Method = 2 subtracted from:

Difference SE of Adjusted
Method of Means Difference T-Value P-Value
3 -9.667 1.727 -5.598 0.0056
4 -9.333 1.727 -5.405 0.0066

Method = 3 subtracted from:

Difference SE of Adjusted
Method of Means Difference T-Value P-Value
4 0.3333 1.727 0.1930 0.9972

From p-values of above , It is seen that The method 3 and 4 are significant from 1 and 2 . Also method 1 and 2 are significant.

Salesman Method Y 1 1 37 2 1 29 3 1 23 1 2 43 2 2 29 3 2 27 1 3 31 2 3 23 3 3 16 1 4 35 2 4 22 3 4 14

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