The Westfall Relocation Company, located in Denver, Colorado, contracts with maj

Question

The Westfall Relocation Company, located in Denver, Colorado, contracts with major corporations forced to lay off employees. Westfall provides a variety of services, including job searches, specialized training and resume development. Westfall then bills the corporation for the services. It currently operates in three regions: west, southwest, and northwest. Recently, Westfall's general manager questioned whether the company's mean billing amount differed by region. To answer this question simple random samples of employees served in these regions have been selected: 10 in the west, 8 in the southwest, and 12 in the northwest. The following sample data were collected West $3,700 2,900 4,100 4,900 4,900 5,300 2,200 3,700 4,800 3,000 Southwest $3,300 2,100 2,600 2,100 3,600 2,700 4,500 2,400 Northwest $2,900 4,300 5,200 3,300 3,600 3,300 3,700 2,400 4,400 3,300 4,400 One factor ANOVA Mean 3,950.0 2,912.5 3,666.7 3,560.0 Std. Dev 1,030.91 West 10 12 30 833.99 Southwest 777.33 Northwest 948.54 Total ANOVA table MS Source Treatment Error Total 2 2.505,791.667ae 27 780,756.173 df 3.21 0562 21,080,416.67 26,092,000.00 29 Post hoc analysis Tukey simultaneous comparison t-values (d.f. 27 Southwest 2,912.5 Northwest 3,666.7 West 3,950.0 Southwest Northwest West 2,912.5 3,666.7 3,950.0 1.87 2.48 0.75 critical values for experimentwise error rate 0.05 0.01 2.49 Is there a significant difference in the mean billing amount across the three regions? Do a complete and appropriate hypothesis test using a.05, the 5-step procedure and p-value approach. Also, if and only if it is appropriate to do so, determine which region(s) is/are have significantly different mean billing amounts and briefly summarize your results in a paragraph

Explanation / Answer

Step 1: State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H0: The company’s mean billing amount is same for all three regions.

Ha: The company’s mean billing amount differed for atleast one region.

Step 2: Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a otest of the nne-way ANOVA test for null hypothesis.

Step 3: Analyze sample data. Based on the output F statistic is 3.21 and p-value for F statistic is 0.0562.

Step 4: Interpret results. Since the P-value (0.0562) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Step 5: Conclusion. At 5% significance level, there is no significant evidence that the company’s mean billing amount differed for atleast one region.

As, we fail to reject the null hypothesis and there is no significant difference between company’s mean billing amount for different regions, it is not appropriate to do post-hoc tests to determine which regions have different mean billing amounts.

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