A statistician is being asked to test a new theory that the proportion of population A possessing a given characteristic is greater than the proportion of population B possessing the characteristic.A random sample of 600 from population A has been taken and it is determined that 480 possess the characteristic.A random sample of 700 taken from population B showed that 350 possess the characteristic.The observed z for this is ___.
A)0.300
B)0.624
C)0.638
D)11.22
E)13.42

Question

Quizplus · Accepted Answer

To test the hypothesis, we can use the z-test for the difference in two proportions:

z = (p_A - p_B) / sqrt{p(1-p)[(1/n_A) + (1/n_B)]}

where p = (x_A + x_B) / (n_A + n_B) is the pooled proportion.

Plugging in the given values, we get:

z = (0.8 - 0.5) / sqrt{0.65(0.35)[(1/600) + (1/700)]} = 11.22

Therefore, the observed z is 11.22, which is option D.

A Statistician Is Being Asked to Test a New Theory