Question

You have been promoted to sales manager of a company that manufactures robots used to assemble automobiles. Although your sales force is given a suggested price at which to sell the robots, they have considerable leeway in negotiating the final price. Past sales records indicate that sometimes there is a large difference in the selling prices that sales reps are able to negotiate. You are interested in knowing if this difference is significant or whether this observed difference in selling prices is just due to random variation. You decide to randomly select four sales over the last year for each of your three saes representatives and observe the actual selling prices of the robot. The table below shows the amounts at which the robots sold in thousands of dollars. Based on the result of your survey, can you conclude that there is a significant difference among the average selling peices that the three sales reps have been able to negotiate? Use α = 0.05. For this question, determine if you require one-way or two way ANOVA test. Create the required ANOVA table using Analysis Toolpak and check whether you obtain the same F-critical value (as obtained in the ANOVA table) using Excel formula. State the null and alternative hypothesis for the test, write the decision rule and the decision statement as well.

	Selling Prices- Thousands of dollars
	Salesperson 1	Salesperson 2	Salesperson 3
	10	11	11
	14	16	13
	13	14	12
	12	15	15
Total	49	56	51

Q1a)

Determine if you require a one-way ANOVA or a two-way ANOVA test and create ANOVA table using the information given above.

Q2b)

Calculate F-critical value using Excel formula and verify that it is the same as obtained in the ANOVA table.

H0

Ha

Decision Rule

Decision Statement

Answer 1

* 1a) One-way ANOVA ANOVA Source of Variation SS Between Groups 6.5 Within Groups 31.5 Total 38 df 2 9 11 MS F 3.25 0.9286 3.5 P-value F crit 0.4299 4.2565 1b) F-critical value using Excel formula: =FINV(0.05,2,9) = 4.2565 Ho: U1 = U2 = 3 Ha: At least one population means differ significantly. Decision Rule: Reject H, if F> 4.2565 Decision Statement: Fail to reject Ho