When the necessary conditions are met, a two-tail test is being conducted to test the difference between two population proportions. The two sample proportions are $\hat { p } _ { 1 }$ = 0.21 and $\hat { p } _ { 2 }$ = 0.15, and the standard error of the sampling distribution of are $\hat { p } _ { 1 }$ - $\hat { p } _ { 2 }$ is 0.018. The calculated value of the test statistic will be:
A) t = -3.33.
B) z = 3.33.
C) t = 3.33.
D) None of these choices are correct.

Question

Quizplus · Accepted Answer

Since the sample sizes are large and the population standard deviations are not known, we can use the z-statistic to test the difference between two population proportions:

z = ((p1 - p2) - (null hypothesis value)) / standard error
= ((0.21 - 0.15) - 0) / 0.018
= 3.33

Therefore, the calculated value of the test statistic is z = 3.33, and the best choice is B.

When the Necessary Conditions Are Met, a Two-Tail Test Is p^1\hat { p } _ { 1 }p^​1​

When the Necessary Conditions Are Met, a Two-Tail Test Is $\hat { p } _ { 1 }$