Calculate chisquare values for the following tables 18 7 25

Calculate chi-square values for the following tables:

18

7

25

16

26

42

34

33

67

Determine whether you would accept or reject the hypothesis of independence for the two variables for the question above.

Calculate conditional and marginal probabilities for the cross-tabulations fo the exercise above and give them an interpretation.

Solution

There are 3 rows and 3 columns

Hence degree of freedom =2x2=4

3 groups each having 3 samples

Create null and alternate hypoteses as follows:

H0: Groups have equal means

Ha: Groups do not have equal means.

Two tailed chi square test.

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Prepare chi square contingency table.

The chi-square statistic is 7.2076. The P-Value is 0.125314. The result is not significant at p < 0.05.

Thus we calculate expected value and then chi square = (o-e)^2/e

Add all of them to get overall chisquare

p value is got from chi square with df 4.

(Expected value e = row total* ijth entry/column total)