A realtor wants to compare the average sales-to-appraisal ratios of residential

Question

A realtor wants to compare the average sales-to-appraisal ratios of residential properties in 4 neighborhoods (A, B, C).

Five properties were randomly selected from each neighborhood and the ratios recorded for each, as shown.

A   

B   

C

1.899

-0.355

1.222

1.646

0.621

1.74

1.94

0.479

1.551

2.528

0.781

1.932

2.69

3.126

2.464

Run the One-way ANOVA (either Excel or JMP) at =0.05 and answer the following questions:

Note: You may still work on this problem on the paper. If so, attach scanned copy of your pages

18. What is the unexplained variance (i.e., variance that is in the sample)?

19. What is the variance explained by the different neighborhoods?What is the F-statistic?

20. Based on these results, what is your conclusion? Explain.

A   

B   

C

1.899

-0.355

1.222

1.646

0.621

1.74

1.94

0.479

1.551

2.528

0.781

1.932

2.69

3.126

2.464

Explanation / Answer

Step 1

Null Hypothesis Ho : µ1 =µ2 =µ3

Alternative Hypothesis : µ1 µ2 µ3

Step 2

Degrees of freedom between = k - 1 = 3 - 1 = 2

Degrees of freedom Within = n - k = 15 - 3 = 12

Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.885

Step 3

Grand Mean = G / N = 2.141+0.93+1.782 / 3 = 1.618

SST = ( Xi - GrandMean)^2 = (1.899-1.618)^2 + (1.646-1.618)^2 + (1.94-1.618)^2 + ……..& so on = 8.417

SS Within = (Xi - Mean of Xi ) ^2 =,(1.899-2.141)^2 + (1.646-2.141)^2 + (1.94-2.141)^2 + ……..& so on = 6.795

SS Between = SST - SS Within = 8.417 - 6.795 = 1.622

Step 4

Mean Square Between = SS Between / df Between = 1.622/2 = 0.811

Mean Square Within = SS Within / df Within = 6.795/12 = 0.566

Step 5

F Cal = MS Between / Ms Within = 0.811/0.566 = 1.432

We got |F cal| = 1.432 & |F Crit| =3.885

MAKE DECISION

Hence Value of |F cal| < |F Crit|and Here We Accept Ho

we have evidence that there is no significance diffence between the treatments

Treatments ONE WAY ANOVA Mean = X /n A 1.899 1.646 1.94 2.528 2.69 2.141 B -0.355 0.621 0.479 0.781 3.126 0.93 C 1.222 1.74 1.551 1.932 2.464 1.782

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