Similar to problem 11.7 in the text, based on section 11.2 of the text. An indiv

Question

Similar to problem 11.7 in the text, based on section 11.2 of the text. An individual owns 3 automobile dealerships and is interested in determining whether average daily sales for the 3 dealerships are the same A random selection of daily sales at the 3 dealerships is presented in the table below. State the appropriate null and alternative hypotheses for this analysis. What is the between-column (explained) variance? Report the Mean Square Error (MSE) for this ANOVA? What is the value of the test-statistic for the test specified above? What are the degrees of freedom for the hypothesis that average sales for each dealership are equal? a. 2 for numerator. 9 for denominator b. 9 for numerator. 2 for denominator c. 2 for numerator. 11 for denominator d. 11 for numerator. 9 for denominator In testing the hypothesis that average sales for each dealership arc equal, the appropriate conclusion to be drawn would be: a. reject H_0 at the 10% significance level. b. the test is significant at the 88% level. c. the test is not significant at the 5% level. d. cannot reject the null hypothesis at the 10% level. c. accept the null hypothesis at the 88% level. What is the critical value for this test if the decision maker is willing to take a 10% chance of error? In one sentence, make a statement to interpret the results of this analysis.

Explanation / Answer

Part-1

Null hypothesis H0: Mu1=Mu2=Mu3

Alternative hypothesis H1: at least one pair of mean is different

Here Mu1,Mu2,Mu3 are the true population mean daily sales for the dealerships 1,2,3 respectively.

Part-3

The between column explained variance=MS between groups=1.1667

Part-4

MSE=8.9630

Part-5

Test statistic F=0.1302

Part-6

Degree of freedom of numerator=2

Degree of freedom of denominator=9

Part-8

p-value=0.8796 =0.88

as p-value=0.88>0.10, we can not reject the null hypothesis at 10% level

Part-9

Critical value =F(0.10,2,9)=3.0065 using excel function =FINV(0.1,2,9)

Part-10

We conclude that the true population mean daily sales for the dealerships 1,2,3 are not different and sales is almost same in all 3 dealerships

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