Question

More online sales Refer to Exercise 35. Calculate and interpret the standard error of$\hat{p}=\frac{x}{n}$ for these data.

Short answer

The value of standard error is$0.0059$.

Step-by-step solution

Given Information

It is given that:

$n=4579$

$x=914$

Concept Used

Formula to be used is$S{E}_{\hat{p}}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Simplification

Sample proportion is calculated as $\hat{p}=\frac{x}{n}$

$=\frac{914}{4579}=0.1996$

Hence, standard error is $S{E}_{\hat{p}}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

$S{E}_{\hat{p}}=\sqrt{\frac{0.1996(1-0.1996)}{4579}}$

$\Rightarrow S{E}_{\hat{p}}=0.0059$