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

Answer:

The confidence interval is (0.444 ± 0.111).

Step-by-step explanation:

The general form of a confidence interval for single proportion is: $(\hat p- E$

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),

$2\hat p=0.888\\\hat p=\frac{0.888}{2}\\ =0.444$

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,

$(0.444-0.111$