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 142 Canadian geese and found that 59 were infected with the parasite.

Use this data to find the lower limit of a 98% confidence interval for the true proportion of Canadian geese that are affected by the parasite. Give your answer rounded to 4 decimal places.

Answer 1

The critical value is obtained using STATKEY (image attached for reference). The 98% lower bound for proportion is given by the formula mentioned.

59 -0.4549 142 In the given question, À Sproportion of Canadian geese affected by parasite for proportion given ley hower bound C.I is the formula, IPCI- < P n Lower bound 98% C. I for proportion Source - SIATKEY Ia Z 0.02 20.02 = -2.054 ده Cimage attached) So, 2.054 0.41549 x 0.58451 0.41549 < P 142 0.3305 <p Lower limit of 98.1 C. I for true proportion of Canadian gerese = 0.3305 that are affected by the parasite