Question

A researcher is interested in estimating the prevalence of Hepatitis C among a group of heroin addicts that routinely have been seeking treatment for their disease at a local hospital. Suppose the researcher estimates that, based on the evidence in previous studies examining this very relationship, 24.7% of intravenous drug users are Hepatitis C positive. What is the margin of error for a 95% confident sample of size 14

Option A:

0.226

Option B:

0.335

Option C:

0.717

Answer 1

Solution :

Given that,

n = 14

Point estimate = sample proportion = = 0.247

1 - = 1 - 0.247 = 0.753

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.247 * 0.753) / 14)

= 0.226

Margin of error = E = 0.226

Option A)