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ANOVA testing

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I have an essay to write, about this statistics problem. I have used several calculation methods and I have no idea where to begin with this problem. I am having difficulty as is with this class. Could you please break down the problem step by step and please explain why I would go with that option to resolve the problem. I have a real problem with why I should do this and that with statistics.

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Solution Summary

Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.

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Cases
A. Century National Bank
Refer to the description of Century National Bank at the end of the Review
The bank has branch offices in four different cities: Cincinnati, Ohio; Atlanta, Georgia; Louisville, Kentucky; and Erie, Pennsylvania. Mr. Selig would like to know whether there is a difference in the mean checking account balances among the four branches. If there are differences, between which branches do these differences occur?

Answer
The null hypotheis tested is
H0: There is no significant difference in the mean checking amount among the four branches.

The alternative hypothesis is

H1: There is significant difference in the mean checking amount among the four branches.

The test statistic used is : F Test (ANOVA)

Rejection critiria: reject the null hypothesis, if the calculated value of F is greater than the critical value of F at 0.05 significance ...

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