Testing the hypothesis - chi square test, Financial Management

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Testing the Hypothesis

To test the null hypothesis, we compare the observed and the expected frequencies. If the actual and the expected values are nearly equal to each other we accept the null hypothesis and if there is a large difference between the two values we reject the null hypothesis. This is what we do as far as observation of the data is concerned and then reaching a conclusion. But mathematically, we employ the chi square statistic given by

1083_chi square test formula.png

where,

f_o is the observed frequency

f_e is the expected frequency.

If this value happens to be smaller, then we conclude that there is a little difference between the actual and the expected frequencies and if the difference is larger, then we conclude that the actual and the expected values are not equal. This is identical to the conclusion where we reach by observing the data. Further this value is compared with the value obtained from the table. We look at how the value is obtained from the table.

f_o	f_e	f_o - f_e	(f_o - f_e)²	(f_o - f_e)²/(f_e)

400	475	-75	5625	11.84
550	475	75	5625	11.84
450	475	-25	625	1.32
500	475	25	625	1.32
600	525	75	5625	10.71
450	525	-75	5625	10.71
550	525	25	625	1.19
500	525	-25	625	1.19

Total				50.12

The value of the Chi Square Statistic is 506_chi square test formula1.png = 50.12.

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