Question

Independent random samples of sizes n1 = 407 and n2 = 307 were taken from two populations. In the first sample, 118 of the individuals met a certain criteria whereas in the second sample, 163 of the individuals met the same criteria. Test the null hypothesis H0:p1=p2versus the alternative hypothesis HA:p1≠p2. What is the value of the z test statistic, testing the null hypothesis that the population proportions are equal? Round your response to at least 2 decimal places.

Answer 1

Sample proportion 1 = 118 / 407 = 0.2899, 2 = 163 / 307 = 0.5309

Pooled proportion = (x1 +x2) / (n1 + n2)

= (118 + 163 ) / (407 + 307)

= 0.3936

Test statistics

z = (1 - 2) / sqrt [ ( 1 - ) * (1 / n1 + 1 / n2) ]

= (0.2899 - 0.5309) / sqrt [ 0.3936 * ( 1 - 0.3936) * ( 1 / 407 + 1 / 307) ]

= -6.5257