Question

Use the given confidence interval limits to find the point estimate and the margin of error E.

Answer 1

Answer:

The point estimate = 0.507

Margin error of  a given confidence interval = 0.032

Step-by-step explanation:

The point estimate is calculated by using the sample statistics of a population.

Thus; point estimate can be expressed with the formula:

$\overline x = \dfrac{\sum \limits ^n _{i=1} \ x _i}{n}$

Given that : 0.475 < p < 0.539

$\overline x = \dfrac{0.475+0.539}{2}$

$\overline x = \dfrac{1.014}{2}$

$\overline x = 0.507$

The point estimate = 0.507

The margin of error  which shows  the percentage of points that the derived results would differ from that of the given population value can be calculated with the formula:

Margin error of  a given confidence interval = $\mathtt{\dfrac{upper \ confidence \ limit - lower \ confidence \ limit }{2}}$

Margin error of  a given confidence interval =  $\dfrac{0.539-0.475}{2}$

Margin error of  a given confidence interval = $\dfrac{0.064}{2}$

Margin error of  a given confidence interval = $0.032$