Testing the hypothesis - chi square test, Financial Management

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,

         fo is the observed frequency

         fe 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.

fo

fe

       fo - fe

      (fo - fe)2

(fo - fe)2/(fe)


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.

Posted Date: 9/15/2012 5:59:07 AM | Location : United States







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