Answer:
The confidence interval is (0.444 ± 0.111).
Step-by-step explanation:
The general form of a confidence interval for single proportion is: [tex](\hat p- E<p<p\hat + E)=\hat p \pm E[/tex]
The interval provided is: (0.333 < p < 0.555)
Then
[tex]\hat p-E=0.333...(i)\\\hat p + E = 0.555...(ii)[/tex]
Solving the two equation simultaneously:
Add (i) and (ii),
[tex]2\hat p=0.888\\\hat p=\frac{0.888}{2}\\ =0.444[/tex]
Substitute the value of [tex]\hat p[/tex] in (i) to compute the value of E:
[tex]\hat p-E=0.333\\0.444-E=0.333\\E=0.444-0.333\\=0.111[/tex]
Thus, the confidence interval is,
[tex](0.444-0.111<p<0.444+0.111)=0.444 \pm 0.111[/tex]
