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 p1 = 0.25 and p2 = 0.20 and the standard error of the sampling distribution of $\hat { p } _ { 1 } - \hat { p } _ { 2 }$ 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.

Question

Quizplus · Accepted Answer

The test statistic for the difference between two proportions is calculated using the formula $Z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{SE}$, where $SE$ is the standard error of the sampling distribution of $\hat{p}_1 - \hat{p}_2$. Assuming the null hypothesis implies $p_1 = p_2$, the formula simplifies to $Z = \frac{\hat{p}_1 - \hat{p}_2}{SE}$. Plugging in the given values, $Z = \frac{0.25 - 0.20}{0.04} = \frac{0.05}{0.04} = 1.25$.

When the Necessary Conditions Are Met, a Two-Tail Test Is p^1−p^2\hat { p } _ { 1 } - \hat { p } _ { 2 }p^​1​−p^​2​

When the Necessary Conditions Are Met, a Two-Tail Test Is $\hat { p } _ { 1 } - \hat { p } _ { 2 }$