Mr. Zobus would also like to know if there is a statistical difference in the me

Question

Mr. Zobus would also like to know if there is a statistical difference in the mean checking account balances among the four branches. If there are differences, between which branches do these differences occur? Use various statistical techniques to evaluate the entire data base, as well as, if overall statistical differences are found, an evaluation of the two or three branches which may be individually different. (ALSO how do you enter this on ANOVA in excel?)

Balance ATM Services Debit Interest City 1756 13 4 0 1 2 748 9 2 1 0 1 1501 10 1 0 0 1 1831 10 4 0 1 3 1622 14 6 0 1 4 1886 17 3 0 1 1 740 6 3 0 0 3 1593 10 8 1 0 1 1169 6 4 0 0 4 2125 18 6 0 0 2 1554 12 6 1 0 3 1474 12 7 1 0 1 1913 6 5 0 0 1 1218 10 3 1 0 1 1006 12 4 0 0 1 2215 20 3 1 0 4 137 7 2 0 0 3 167 5 4 0 0 4 343 7 2 0 0 1 2557 20 7 1 0 4 2276 15 4 1 0 3 1494 11 2 0 1 1 2144 17 3 0 0 3 1995 10 7 0 0 2 1053 8 4 1 0 3 1526 8 4 0 1 2 1120 8 6 1 0 3 1838 7 5 1 1 3 1746 11 2 0 0 2 1616 10 4 1 1 2 1958 6 2 1 0 2 634 2 7 1 0 4 580 4 1 0 0 1 1320 4 5 1 0 1 1675 6 7 1 0 2 789 8 4 0 0 4 1735 12 7 0 1 3 1784 11 5 0 0 1 1326 16 8 0 0 3 2051 14 4 1 0 4 1044 7 5 1 0 1 1885 10 6 1 1 2 1790 11 4 0 1 3 765 4 3 0 0 4 1645 6 9 0 1 4 32 2 0 0 0 3 1266 11 7 0 0 4 890 7 1 0 1 1 2204 14 5 0 0 2 2409 16 8 0 0 2 1338 14 4 1 0 2 2076 12 5 1 0 2 1708 13 3 1 0 1 2138 18 5 0 1 4 2375 12 4 0 0 2 1455 9 5 1 1 3 1487 8 4 1 0 4 1125 6 4 1 0 2 1989 12 3 0 1 2 2156 14 5 1 0 2

Explanation / Answer

To carry ANOVA in Excel,

enter the balances data for each city in different columns like this

Then, load the Add-In XLMiner Analysis ToolPack

In ANOVA,

enter the input and output ranges

The data is grouped by rolumns

With labels in first row.

Results of ANOVA from Excel:

The p-value of the F-statistic test for comparing the means between the 4 cities is 0.014, which is less than the significance level of 0.05

Thus, we reject the null hypothesis that the mean account balances is equal in the 4 branches.

Thus, overall differences in mean account checking balances are found to be statistically significant.

So, we carry out a multiple comparison test using Scheffe's method.

The results are:

Multiple Comparisons

Dependent Variable:   Balance

Scheffe

(I) City

(J) City

Mean Difference (I-J)

Std. Error

Sig.

95% Confidence Interval

Lower Bound

Upper Bound

1

2

-598.272*

194.455

.032

-1158.77

-37.77

3

-77.982

204.306

.986

-666.88

510.91

4

-142.087

208.455

.926

-742.94

458.77

2

1

598.272*

194.455

.032

37.77

1158.77

3

520.290

201.483

.096

-60.47

1101.05

4

456.186

205.688

.191

-136.69

1049.06

3

1

77.982

204.306

.986

-510.91

666.88

2

-520.290

201.483

.096

-1101.05

60.47

4

-64.104

215.026

.993

-683.90

555.69

4

1

142.087

208.455

.926

-458.77

742.94

2

-456.186

205.688

.191

-1049.06

136.69

3

64.104

215.026

.993

-555.69

683.90

*. The mean difference is significant at the 0.05 level.

Thus, the mean differences between the balances of branch 1 and branch 2 is statistically significant

whereas the mean differences in the balances of other pair of branches are not statistically significant.

Thus, the homogeneous subset of groups with similar balances are:

Balance

Scheffea,b

City

N

Subset for alpha = 0.05

1

2

1

16

1281.38

3

14

1359.36

1359.36

4

13

1423.46

1423.46

2

17

1879.65

Sig.

.923

.105

Means for groups in homogeneous subsets are displayed.

1 2 3 4 748 1756 1831 1622 1501 2125 740 1169 1886 1995 1554 2215 1593 1526 137 167 1474 1746 2276 2557 1913 1616 2144 634 1218 1958 1053 789 1006 1675 1120 2051 343 1885 1838 765 1494 2204 1735 1645 580 2409 1326 1266 1320 1338 1790 2138 1784 2076 32 1487 1044 2375 1455 890 1125 1708 1989 2156

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