Question

Using the following dataset, conduct a one-way ANOVA and post-hoc comparisons if necessary.   A real estate developer is considering investing in a shopping mall on the outskirts of Atlanta, GA. Three parcels of land are being evaluated. Of particular importance is the income in the area surrounding the proposed mall. A random sample of four families is selected near each proposed mall. The following are the sample results. At the 0.05 significance level, can the developer conclude there is a difference in the mean income?

Southwyck Area (in $1,000’s) (Group 1)	Franklin Park (in $1,000’s) (Group 2)	Old Orchard (in $1,000’s) (Group 3)
64	74	75
68	71	80
70	69	76
60	70	78

1. (2 points) What is the F-value for the one-way ANOVA test:

a. 18.14

b. 14.18

c. 138.25

d. None of the above

2. (2 points) What is the p-value:

a. 0.0071

b. 14.18

c. 0.0017

d. None of the above

3. (2 points) What is the mean for Group 1:

a. 65.5

b. 71.0

c. 77.3

d. None of the above

4. (2 points) What is the mean for Group 2:

a. 65.5

b. 71.0

c. 77.3

d. None of the above

5. (2 points) What is the mean for Group 3:

a. 65.5

b. 71.0

c. 77.3

d. None of the above

6. (2 points) Is there a difference mean income between at least two of the areas?

a) TRUE     b) FALSE

7. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 1 significantly different from Group 2?  

a) TRUE     b) FALSE

8. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 2 significantly different from Group 3?  

a) TRUE     b) FALSE

9. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 1 significantly different from Group 3?  

a) TRUE     b) FALSE

Using the following dataset, conduct a one-way ANOVA and post-hoc comparisons if necessary.   The following is sample information. Test the hypothesis that all treatment means are equal at the 0.05 significance level.

Treatment 1 (Group 1)	Treatment 2 (Group 2)	Treatment 3 (Group 3)
8	3	3
6	2	4
10	4	5
9	3	4

10. (2 points) What is the F-value for the one-way ANOVA test:

a. 21.94

b. 14.18

c. 31.083

d. None of the above

11. (2 points) What is the p-value:

a. 0.01

b. 0.05

c. 0.03

d. None of the above

12. (2 points) What is the mean for Group 1:

a. 3.0

b. 4.0

c. 5.1

d. None of the above

13. (2 points) What is the mean for Group 2:

a. 3.0

b. 4.0

c. 5.1

d. None of the above

14. (2 points) What is the mean for Group 3:

a. 3.0

b. 4.0

c. 5.1

d. None of the above

15. (2 points) Is there a difference mean income between at least two of the treatment groups?  

a) TRUE     b) FALSE

16. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 1 significantly different from Group 2?  

a) TRUE     b) FALSE

17. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 2 significantly different from Group 3?  

a) TRUE     b) FALSE

18. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 1 significantly different from Group 3?  

a) TRUE     b) FALSE

Use the following dataset for the next four questions:

X:     5     3     6     3     4     4     6     8

Y:    13    15    7    12    13    11    9    5

19. (3 points) What is the Pearson correlation value r(x,y)?   r = _________

a. -0.98

b. -0.89

c. 0.89

d. None of the above

20. (3 points) Is the “r” signifcant at alpha = 0.05?

a) TRUE    

b) FALSE

21. (4 points) Identify the regression equation below

a. Y = 19.12 + 1.74(X)

b. Y = 19.12 – 1.74(X)

c. Y = -4.802 – 1.74(X)

d. None of the above

22. (3 points) Calculate the value of Y when X is 7:   

a. 9.64

b. 4.96

c. 6.94

d. None of the above

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales (in thousands $) last month for each client sampled.

Number of Contacts (X)	Sales (in thousands $) Y
14	24
12	14
20	28
16	30
46	80
23	30
48	90
50	85
55	120
50	110

23. (4 points) Identify the regression equation below :

a. Sales = -12.2 + 2.19(Contacts)

b. Sales = 2.19 – 12.2(Contacts)

c. Sales = 6.56 + 0.176(Contacts)

d. None of the above

24. (3 points) Calculate the estimated sales if 40 contacts are made:  

a. Approximately 57

b. Approximately 75

c. Approximately 85

d. Approximately 105

Answer 1

using minitab>stat>ANOVA >One way

we have

One-way ANOVA: Group 1, Group 2, Group 3

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 3 Group 1, Group 2, Group 3

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 276.50 138.250 14.18 0.002
Error 9 87.75 9.750
Total 11 364.25

Model Summary

S R-sq R-sq(adj) R-sq(pred)
3.12250 75.91% 70.56% 57.17%

Means

Factor N Mean StDev 95% CI
Group 1 4 65.50 4.43 (61.97, 69.03)
Group 2 4 71.00 2.16 (67.47, 74.53)
Group 3 4 77.25 2.22 (73.72, 80.78)

Pooled StDev = 3.12250

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean Grouping
Group 3 4 77.25 A
Group 2 4 71.00 B
Group 1 4 65.50 B

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value P-Value
Group 2 - Group 1 5.50 2.21 (-0.67, 11.67) 2.49 0.080
Group 3 - Group 1 11.75 2.21 ( 5.58, 17.92) 5.32 0.001
Group 3 - Group 2 6.25 2.21 ( 0.08, 12.42) 2.83 0.047

Individual confidence level = 97.91%

Ans 1 )What is the F-value for the one-way ANOVA test:

b. 14.18

2. (2 points) What is the p-value:

c. 0.0017

3. (2 points) What is the mean for Group 1:

a. 65.5

4. (2 points) What is the mean for Group 2:

b. 71.0

5. (2 points) What is the mean for Group 3:

c. 77.

6. (2 points) Is there a difference mean income between at least two of the areas?

a) TRUE   

7. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 1 significantly different from Group 2?  

b) FALSE

8. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 2 significantly different from Group 3?  

a) TRUE

9. (2 points) Using the results of the Tukey test (alpha = 0.05), is Group 1 significantly different from Group 3?  

a) TRUE

using minitab>stat>Regresion

we have

Regression Analysis: y versus x

The regression equation is
y = 19.12 - 1.743 x

S = 1.65786 R-Sq = 79.4% R-Sq(adj) = 75.9%

Analysis of Variance

Source DF SS MS F P
Regression 1 63.3840 63.3840 23.06 0.003
Error 6 16.4910 2.7485
Total 7 79.8750

19. (3 points) What is the Pearson correlation value r(x,y)?   r = _________

b. -0.8

20. (3 points) Is the “r” signifcant at alpha = 0.05?

a) TRUE    

21. (4 points) Identify the regression equation below

b. Y = 19.12 – 1.74(X)

22. (3 points) Calculate the value of Y when X is 7:   

c. 6.94

using minitab>stat>Regresion

we have

Regression Analysis: Sales (in thousands $) Y versus Number of Contacts (X)

The regression equation is
Sales (in thousands $) Y = - 12.20 + 2.195 Number of Contacts (X)

S = 9.31045 R-Sq = 95.1% R-Sq(adj) = 94.5%

Analysis of Variance

Source DF SS MS F P
Regression 1 13555.4 13555.4 156.38 0.000
Error 8 693.5 86.7
Total 9 14248.9

1. (4 points) Identify the regression equation below :

a. Sales = -12.2 + 2.19(Contacts)

24. (3 points) Calculate the estimated sales if 40 contacts are made:  

b. Approximately 75