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House Type Appraiser 1 2 3 Cape Cod 425 415 430 Colonial 530 550 540 Ranch 390 4

ID: 3371236 • Letter: H

Question

House Type

Appraiser

1

2

3

Cape Cod

425

415

430

Colonial

530

550

540

Ranch

390

400

380

House Type

Appraiser

1

2

3

Cape Cod

425

415

430

Colonial

530

550

540

Ranch

390

400

380

2eNov Refer to Chapter 13 problem 41 on p. 457. Refer to Houses data on Connect or Webcam pus. At the 5% significance level, can you conclude that the a differ by appraiser? (20 points) 2. verage values State the hypothesis: What is the test statistic? What is the critical value rejection rule? What is the p-value? What is the p-value rejection rule? What is the decision to the test? Interpret your decision: Note. Attach Excel output that shows the test results. Hint: thesame output is used for #2

Explanation / Answer

Solution:

Here, we have to use two way analysis of variance or two way ANOVA F test for checking the given hypothesis. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: The average values do not differ by appraiser.

Alternative hypothesis: Ha: The average values differ by appraiser.

We are given 5% level of significance. ? = 0.05

The test statistic for this test is given as below:

F = MS treatment / MS error

The test statistic value from excel output is given as below:

F for row = 0.325

F for column = 167.5

The critical value for this test is given as below:

Critical value F = 6.944272

(Critical value is calculated by using excel or F-table. Excel command: =Finv(0.05,2,4). ? = 0.05, df1 = 2, df2 = 4)

Rejection rule:

We reject the null hypothesis if the test statistic value is more than critical value, otherwise we do not reject the null hypothesis.

We reject the null hypothesis if the p-value is less than the alpha value 0.05, otherwise we do not reject the null hypothesis.

Excel data and output for this ANOVA is given as below:

House Type

Appraiser

Cape Cod

Colonial

Ranch

1

425

530

390

2

415

550

400

3

430

540

380

Anova: Two-Factor Without Replication

SUMMARY

Count

Sum

Average

Variance

1

3

1345

448.3333

5308.333

2

3

1365

455

6825

3

3

1350

450

6700

Cape Cod

3

1270

423.3333

58.33333

Colonial

3

1620

540

100

Ranch

3

1170

390

100

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Rows

72.22222

2

36.11111

0.325

0.73997

6.944272

Columns

37222.22

2

18611.11

167.5

0.000139

6.944272

Error

444.4444

4

111.1111

Total

37738.89

8

P-value for rows is given as 0.73997 > ? = 0.05, so we do not reject the null hypothesis that average values do not differ by appraiser.

There is sufficient evidence to conclude that average values do not differ by appraiser.

P-value for column is given as 0.000139 < ? = 0.05, so we reject the null hypothesis that average values do not differ by house type.

There is sufficient evidence to conclude that average values are differ by house type.

House Type

Appraiser

Cape Cod

Colonial

Ranch

1

425

530

390

2

415

550

400

3

430

540

380