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)-1.6286.

Question

Quizplus · Accepted Answer

We can use the test statistic formula for testing the equality of population proportions, which is:

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

Where:
p1 = proportion of successes in population 1
p2 = proportion of successes in population 2
p = pooled proportion = (x1 + x2) / (n1 + n2)
x1 = number of successes in sample 1
x2 = number of successes in sample 2
n1 = sample size of sample 1
n2 = sample size of sample 2

Plugging in the values given in the problem, we get:

p1 = 53/100 = 0.53
p2 = 95/150 = 0.6333
p = (53 + 95) / (100 + 150) = 0.56
n1 = 100, n2 = 150

z = (0.53 - 0.6333) / sqrt [0.56 * (1 - 0.56) * (1/100 + 1/150)]
z = -1.6286

Therefore, the test statistic for testing the equality of population proportions is -1.6286, which is choice (D).

A Sample of Size 100 Selected from One Population Has