For comparing two sample proportions, the test statistic z is often used. But most
software will ask users to carry out a chi-square test for that purpose. The test statistic z is defined as "( pˆ1 - pˆ2) - (P1 - P2)" in its numerator. However, such test is done under a 2x2 chi-square test. A statistical software has produced ?2= 5.024 from 1 pˆ = 0.50 and 2 pˆ = 0.40 with the p-value = 0.05.
(a) Obtain the value of test statistic z from ?2= 5.024.
(b) Find the p-value for testing:
H0: P1 ? P2
HA: P1 < P2