A sample of size 100 selected from one population has 53 successes, and a sample of size 150 selected from a second population has 95 successes. The test statistic for testing the equality of the population proportions is equal to:
A) -11.1051.
B) -17.1107.
C) -0.0944.
D) -1.0944.

Question

Quizplus · Accepted Answer

The formula for calculating the test statistic for testing the equality of population proportions is:

z = (p1 - p2) / sqrt{p(1-p) [(1/n1) + (1/n2)]}

where p = (x1 + x2) / (n1 + n2)

Here, n1 = 100, x1 = 53, n2 = 150, x2 = 95.

Thus,

p1 = x1 / n1 = 0.53 
p2 = x2 / n2 = 0.6333 
p = (x1 + x2) / (n1 + n2) = (53 + 95) / (100 + 150) = 0.5867

So,

z = (0.53 - 0.6333) / sqrt{0.5867(1 - 0.5867)[(1/100) + (1/150)]}

= -1.09 (rounded to two decimal places)

Therefore, the test statistic for testing the equality of the population proportions is -1.0944, which is closest to choice D.

A Sample of Size 100 Selected from One Population Has