Question

Express the confidence interval (0.086 comma 0.130 )in the form of ModifyingAbove p with caret minus Upper E less than p less than ModifyingAbove p with caret plus Upper E.

Answer 1

C.I = 0.108 ± 0.022

Explanation:

In this case, we are given a symmetric confidence interval, and the sample proportion p', is derived by finding the average of the two values.

Therefore, the sample proportion will be:

`p' = (0.086 + 0.130)/(2)`

`= (0.216)/(2)`

= 0.108

p' = 0.108

To find the margin of error, we have:

M.E = ½ * length of confidence interval

Where length of confidence interval = 0.130 - 0.086

= 0.044

Therefore,

`M.E = (1)/(2) * 0.044 = 0.022`

Margin of error = 0.022

The confidence interval is expressed as:

p' ± M.E

= 0.108 ± 0.022