Question

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

0.475

Answer 1

The point estimate = 0.507

Margin error of a given confidence interval = 0.032

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 = (\sum \limits ^n _(i=1) \ x _i)/(n)`

Given that : 0.475 < p < 0.539

`\overline x = (0.475+0.539)/(2)`

`\overline x = (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{(upper \ confidence \ limit - lower \ confidence \ limit )/(2)}`

Margin error of a given confidence interval =
`(0.539-0.475)/(2)`

Margin error of a given confidence interval =
`(0.064)/(2)`

Margin error of a given confidence interval =
`0.032`