Question

Express the confidence interval 0.333 less than p less than 0.555 in the form Modifying Above p with caret plus or minus Upper E. Modifying Above p with caret plus or minus Upper E equals nothing plus or minus nothing

Answer 1

Answer: =
`0.444\pm 0.111`

Explanation:

The confidence interval for population proportion(p) is given by :-

`\hat{p}-E<p<\hat{p}+E` (1)

It is also written as :
`\hat{p}\pm E` (*)

The given confidence interval for population proportion :

`0.333<p<0.555` (2)

Comparing (1) and (2) , we get

Lower limit =
`\hat{p}-E=0.333` (3)

Upper limit =
`\hat{p}+E=0.555` (4)

Adding (3) and (4) , we get

`2\hat{p}=0.888\\\Rightarrow\ \hat{p}=(0.888)/(2)=0.444`

Put value of
`\hat{p}=0.444` in (2) , we get

`0.444+E=0.555\\\\\Rightarrow\ E=0.555-0.444=0.111`

Put values of
`\hat{p}=0.444` and E= 0.111 in (*) , we get

Required form =
`0.444\pm 0.111`