Question

Cercarial dermatitis, commonly known as "swimmer's itch", is a rash caused by an allergic reaction to parasites that burrow into the skin. The parasites are commonly found in waterfowl such as the Canadian goose. A group of researchers examined a random sample of 127 Canadian geese and found that 44 were infected with the parasite. Use this data to find the upper limit of a 94% confidence interval for the true proportion of Canadian geese that are affected by the parasite. Give your answer rounded to 4 decimal places. Answer:

Answer 1

$\widehat p$ = 44/127 = 0.3465

For 94% Confidence interval, the critical value is z^* = 1.88

The upper limit of the 94% confidence interval is

P1-P P + 2* n

$= 0.3465+ 1.88* \sqrt{\frac{0.3465(1 - 0.3465)}{127}}$

= 0.3465 + 0.0794

= 0.4259