Question

(S 11.1) Random samples of sizes n1 = 405 and n2 = 311 were taken from two independent populations. In the first sample, 120 of the individuals met a certain criteria whereas in the second sample, 131 of the individuals met the same criteria. Run a 2PropZtest to test whether the proportions are different, and answer the following questions.

What is the value of p?, the pooled sample proportion?. .3505586 Round your response to at least 3 decimal places

Calculate the z test statistic, for testing the null hypothesis that the population proportions are equal.______________ Round your response to at least 2 decimal places.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ? 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	120	405	131	311	-0.12492557	0.035974861	-3.4725796	0.0005

Hence,

z test statistic = -3.47