Question

# (S 11.1) Random samples of sizes n1 = 405 and n2 = 311 were taken from...

(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.

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
HA : 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