Question

Obtain a formula for the margin of error, $E$, in estimating the difference between two population proportions by referring to Step 2 of Procedure $11.4$on page 472 .

Short answer

The formula of margin of error is$E=z_{\alpha /2}\sqrt{\frac{{\tilde{p}}_1\left(1-{\tilde{p}}_1\right)}{n_1}+\frac{{\tilde{p}}_2\left(1-{\tilde{p}}_2\right)}{n_2}}$

Step-by-step solution

Given information

Given in the question that, We need to obtain a formula for the margin of error, $E$ in estimating the difference between two population proportions by referring to Step 2 of Procedure $11.4$ on page 472 .

Explanation

The given values are$P_1-P_2$

The formula for the margin of error in estimate the difference between two populations Proportions is,

$E=z_{\alpha }/2\sqrt{\frac{{\tilde{p}}_1\left(1-{\tilde{p}}_1\right)}{n_1}+\frac{{\tilde{p}}_2\left(1-{\tilde{p}}_2\right)}{n_2}}$

Define the following variables:

$n_1=$The sample size for the first sample.

$n_2=$The sample size for the second sample .

${\tilde{p}}_1$The sample proportion for the first sample.

${\tilde{p}}_2$The sample proportion for the second sample.

Therefore, the formula of margin of error is

$E=z_{\alpha /2}\sqrt{\frac{{\tilde{p}}_1\left(1-{\tilde{p}}_1\right)}{n_1}+\frac{{\tilde{p}}_2\left(1-{\tilde{p}}_2\right)}{n_2}}$.