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 JMP output of a randomized block ANOVA of these data.

Salesman, j

Sales Method, i A B C

1 32 29` 30

2 31 30 28

3 28 25 23

4 25 24 23

Analysis of Variance

Source DF Sum of Squares Mean Square F Ratio

Model 5 107.33333 21.4667 24.1500

Error 6 5.33333 0.8889 Prob > F

C. Total 11 112.66667 22.3556 0.0007*

Effect Tests

Source Nparm DF Sum of Squares F Ratio Prob > F

Method 3 3 88.666667 33.2500 0.0004*

Salesman 2 2 18.666667 10.5000 0.0110*

Least Squares Means Estimates

Method Estimate Salesman Estimate

1 30.333333 A 29.000000

2 29.666667 B 27.000000

3 25.333333 C 26.000000

4 24.000000

Tukey HSD All Pairwise Comparisons

Quantile = 3.46171, Adjusted DF = 60, Adjustment = Tukey

Method -Method Difference Std Error tRatio Prob>[t]

1 2 0.666667 0.7698004 0.87 0.8221

1 3 5.000000 0.7698004 6.50 0.0026*

1 4 6.333333 0.7698004 8.23 0.0007*

2 3 4.333333 0.7698004 5.63 0.0054*

2 4 5.666667 0.7698004 7.36 0.0013*

3 4 1.333333 0.7698004 1.73 0.3856

Lower 95% Upper 95%

-1.99816 3.331490

2.33518 7.664820

3.66851 8.998160

1.66851 6.998160

3.00184 8.331490

-1.33149 3.998160

a. Test the null hypothesis H0 that no differences exist between the effects of the sales methods (treatments) on mean weekly sales. Set a = 0.5. Can we conclude that the different sales methods have different effects on mean weekly sales?

F = 33.2500, pvalue = 0.0004; _________ H0: there is a ________ in sales methods.

b. Test the null hypothesis H0 that no differences exist between the effects of the salesmen (blocks) on mean weekly sales. Set a = 0.4. Can we conclude that the different salesman have different effects on mean weekly sales?

F = 10.5000, p-value = 0.0110; ___________ H0: salesman __________ 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 3 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: [____________ , ____________]

Method 3 - Method 4: [____________ , ____________]