In the chi-square test of association, as the difference between the observed and expected proportions increases ... a. the chi-square test statistic increases b. the chi-square critical value increases c. the likelihood of rejecting the null hypothesis increases d. the likelihood of rejecting the null hypothesis decreases e. the chi-square critical value decreases f. the chi-square test statistic decreases

Question

Emery George

Mathematics

24 January, 11:56

In the chi-square test of association, as the difference between the observed and expected proportions increases ... a. the chi-square test statistic increases b. the chi-square critical value increases c. the likelihood of rejecting the null hypothesis increases d. the likelihood of rejecting the null hypothesis decreases e. the chi-square critical value decreases f. the chi-square test statistic decreases

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Franklin Johnston · Answer 1

Opton A

Step-by-step explanation:

In the chi-square test of association, as the difference between the observed and expected proportions increases, the chi-square test statistic also increases. This is because if the claim made in the null hypothesis is true: the claim that frequency of the observed is equal to that of the expected (Oi = Ei) then, the observed and the expected values are close to each other and the difference Oi - Ei is small for each category and the chisquare test statistic is small.

But when the observed data does not fit to what is expected as of the null hypothesis, the difference between the observed and expected values, Oi - Ei is large producing a large chi square statistic.