A sample of size 125 selected from one population has 55 successes, and a sample of size 140 selected from a second population has 70 successes. The test statistic for testing the equality of the population proportions is equal to:
A) -0.060.
B) -0.977.
C) -0.940.
D) -0.472.

Question

Quizplus · Accepted Answer

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

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

where p1 and p2 are the population proportions, p̂ is the pooled sample proportion, and n1 and n2 are the sample sizes.

Plugging in the given values, we get:

p̂ = (x1 + x2) / (n1 + n2) = (55 + 70) / (125 + 140) = 0.514

z = (0.55 - 0.5) / sqrt [ (0.514(1-0.514) / 125) + (0.514(1-0.514) / 140) ]
  = 0.05 / sqrt [ 0.00221 + 0.00194 ]
  = 0.05 / sqrt (0.00415)
  = 0.05 / 0.0644
  = -0.977

Therefore, the test statistic for testing the equality of the population proportions is -0.977, which corresponds to choice B.

A Sample of Size 125 Selected from One Population Has