the results of a recent poll on the preference of shoppers regarding two products are shown below. product…
the results of a recent poll on the preference of shoppers regarding two products are shown below. product shoppers surveyed shoppers favoring this product a 800 560 b 900 612 the standard error of p1 - p2 is a..0225. b..044. c..025. d..68.
Answer
Explanation:
Step1: Calculate $\hat{p}_1$ and $\hat{p}_2$
$\hat{p}_1=\frac{560}{800}=0.7$, $\hat{p}_2 = \frac{612}{900}=0.68$
Step2: Use the formula for standard - error of $\hat{p}_1-\hat{p}_2$
The formula for the standard error of $\hat{p}_1 - \hat{p}_2$ is $SE=\sqrt{\frac{\hat{p}_1(1 - \hat{p}_1)}{n_1}+\frac{\hat{p}_2(1 - \hat{p}_2)}{n_2}}$. Substitute $\hat{p}_1 = 0.7$, $n_1 = 800$, $\hat{p}_2=0.68$, $n_2 = 900$ into the formula: [ \begin{align*} SE&=\sqrt{\frac{0.7\times(1 - 0.7)}{800}+\frac{0.68\times(1 - 0.68)}{900}}\ &=\sqrt{\frac{0.7\times0.3}{800}+\frac{0.68\times0.32}{900}}\ &=\sqrt{\frac{0.21}{800}+\frac{0.2176}{900}}\ &=\sqrt{0.0002625 + 0.00024178}\ &=\sqrt{0.00050428}\ &\approx0.0225 \end{align*} ]
Answer:
a. 0.0225