Question

The 1st population's sample has 312 successes and a sample size = 620.

The 2nd population's sample has 398 successes and a sample size = 679.
What is the test statistic (z-score) for this sample? (Round to 3 decimal places.)
test statistic =

Answer 1

Based on the available information, the the test statistic (z-score) for this sample is approximately -2.681.

To calculate the test statistic (z-score) for this sample, use the formula for proportions:

z = (p1 - p2) / √((p * (1 - p)) * ((1 / n1) + (1 / n2)))

Where:

p1 and p2 are the sample proportions

n1 and n2 are the sample sizes

p is the pooled proportion

Given the sample information:

For the 1st population's sample:

Number of successes (p1) = 312

Sample size (n1) = 620

For the 2nd population's sample:

Number of successes (p2) = 398

Sample size (n2) = 679

First, let's calculate the pooled proportion (p):

p = (p1 + p2) / (n1 + n2)

p = (312 + 398) / (620 + 679)

p ≈ 0.536

Now, we can calculate the test statistic (z-score):

z = (p1 - p2) / √((p * (1 - p)) * ((1 / n1) + (1 / n2)))

z = (312/620 - 398/679) / √((0.536 * (1 - 0.536)) * ((1 / 620) + (1 / 679)))

z ≈ (-0.0516) / √(0.249 * (0.751) * (0.003226 + 0.002942))

z ≈ (-0.0516) / √(0.000186 + 0.000184)

z ≈ (-0.0516) / √(0.00037)

z ≈ (-0.0516) / 0.01924

z ≈ -2.681

Rounding to 3 decimal places, the test statistic (z-score) for this sample is approximately -2.681.