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 and , and the standard error of the sampling distribution of is 0.04. The calculated value of the test statistic will be:
A) z = 0.25
B) z = 1.25
C) t = 0.25
D) t = 0.80
E) t = 1.25

Question

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  and  , and the standard error of the sampling distribution of  is 0.04. The calculated value of the test statistic will be:
A) z = 0.25 
B) z = 1.25 
C) t = 0.25 
D) t = 0.80 
E) t = 1.25

Quizplus · Accepted Answer

Since the standard error of the sampling distribution is given and the sample size is not provided, we can conclude that the sample size is sufficiently large (n > 30) for the Central Limit Theorem to apply. Therefore, we can use a z-test statistic.

The formula for the z-test statistic for testing the difference between two population proportions is:

z = (p1 - p2) / SE

where p1 and p2 are the sample proportions, and SE is the standard error of the sampling distribution.

Substituting the given values, we get:

z = (0.35 - 0.3) / 0.04
z = 1.25

Therefore, the calculated value of the test statistic is z = 1.25, which corresponds to choice B.

When the Necessary Conditions Are Met, a Two-Tail Test Is