Team+B+RES342+Week+4+Nonparametric+Statistical+Analysis+of+Account+Balances+vs.+Cities+FINAL

# 821e 14 p value step four formulate a decision rule

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8.21E-14 p-value Step Four – Formulate a Decision Rule The fourth step in the five-step hypothesis test is to formulate a decision rule. The Kruskal-Wallis test is a right-tailed test, and the team will reject the null hypothesis if H is greater than the critical value. The test statistic follows a chi-square distribution so the degrees of freedom equal c-1. In this study, the degrees of freedom equal 8-1=7. The team can use Microsoft Excel to calculate the critical value for the test, using =CHIINV(α, df ). In this test, the input is =CHIINV(0.05, 7 ). The critical value is 14.07 pulled from Appendix E for Chi- Squared Crit-cal Value table for a right-tailed test. This means that the team will reject the null hypothesis if H > 14.07. Step Five – Make a Decision The final step is to make a decision. The team input values from Table into Equation 1 to calculate the value of H . The team calculated the value of H , which is 76.192. In this test, H is greater than 14.07, which means that the team should reject the null hypothesis. In other words,

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the team can conclude that all four cities do not have the same balances. The team also calculated the p-value using Microsoft Excel. The Microsoft Excel formula for calculating the p -value is = CHIDIST(χ 2 , df ). The input to Microsoft Excel for this study was =CHIDIST(14.07, 7). The resulting p -value is 8.21E-14. Why the Kruskal-Wallis Test The nonparametric test that Team B has chosen was the Kruskal-Wallis test because it compares two independent samples, and the groups can be of different sizes if each has five or more observations (Doane & Seward, 2007). The reason Research Team B chose the Kruskal- Wallis test is because it is comparable to the Week 3 ANOVA test. Moreover, the K-W Test requires that the populations be of similar shape, but does not require normal population as in ANOVA which suits the data. The K-W Test also is suitable to finances and financial data (Doane & Seward, 2007). The Results, Interpretation, and Difference from Week 3 The results of doing this Kruskas-Wallis Test are shown that all four cities do not have the same median or mean balances. The Kruskas-Wallis Test equation requires researchers to find the value of H. The value of H is 76.192, which was greater than 14.07 and resulting in a rejection of the null hypothesis leading researchers to conclude that at least one of the four sample cities has a different median account balance. Looking over the results from Week there is no differences in the test. In both tests, the test statistics exceeded the critical values, resulting in the rejection of the null hypothesis. Conclusion With the results of the two different tests taken by Team B from this data, researchers’ analysis shows that the null hypothesis should be rejected for the parametric and nonparametric
test. Each set of data used in the cities chosen was deemed to have different results and the bank accounts did not have equal means or medians in all cities. It is safe to say that determining whether bank balances have equal mean or median values in each city is research that has many independent, moderate, and intervening variables.

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References Anguay, H., Pittendrigh J. Thorson, J., and Ward, S. (2011). A Research Study of Account Balances vs. Interest . Research and Evaluation II. University of Phoenix. Anguay, H., Pittendrigh J. Thorson, J., and Ward, S. (2011) A Statistical Analysis of Bank Account Balances and Cities. Research and Evaluation II. University of Phoenix. Doane, D. P. and Seward, L.E. (2007). Applied Statistics in Business and Economics. McGraw- Hill. Lind, Marchal, and Wathen. (2008). Century National Bank Data Set. Statistical Techniques in Business & Economics, 13th edition. New York, NY: McGraw-Hill.
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• Spring '12
• ALL
• Statistics, Null hypothesis, Statistical hypothesis testing, Non-parametric statistics, Doane

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