Problem 21BB

Equivalent Tests A χ2 test involving a 2 × 2 table is equivalent to the test for the difference between two proportions, as described in Section 9-2. Using the claim and table in Example 1, verify that the χ test statistic and the z test statistic (found from the test of equality of two proportions) are related as follows: z2 = χ2 . Also show that the critical values have that same relationship.

Example 1 Are Four Quarters the Same as One Dollar?

Solution 21BB

Similarly, the critical value of chi square statistic at 0.05significance level is 3.841, also the critical value for z statistic is. Thus we can say that holds good for critical values also. Thus,