Question

Express the confidence interval 0.333less thanpless than0.555 in the form ModifyingAbove p with caret plus or minus Upper E. ModifyingAbove p with caret plus or minus Upper Eequals nothingplus or minus nothing

Answer 1

The confidence interval is (0.444 ± 0.111).

Explanation:

The general form of a confidence interval for single proportion is:
`(\hat p- E<p<p\hat + E)=\hat p \pm E`

The interval provided is: (0.333 < p < 0.555)

Then

`\hat p-E=0.333...(i)\\\hat p + E = 0.555...(ii)`

Solving the two equation simultaneously:

Add (i) and (ii),

`2\hat p=0.888\\\hat p=(0.888)/(2)\\ =0.444`

Substitute the value of
`\hat p` in (i) to compute the value of E:

`\hat p-E=0.333\\0.444-E=0.333\\E=0.444-0.333\\=0.111`

Thus, the confidence interval is,

`(0.444-0.111<p<0.444+0.111)=0.444 \pm 0.111`