A researcher wishes to estimate the proportion of fish in a certain lake that is inedible due to pollution of the lake.How large a sample should be tested in order to be 99% confident that the true proportion of inedible fish is estimated to within 6%?

A) 188
B) 461
C) 376
D) 267
E) Not enough information is given.

Question

Mercedes Bailey · Accepted Answer

Final Answer : B, Explanation :  We need to use the formula n = (z^2 * p * q)/E^2 where:- n is the sample size we need to find- z is the z-score associated with the desired level of confidence (99% in our case, so z = 2.58)- p is the estimated proportion of inedible fish (unknown, we'll have to use 0.5 to get the maximum sample size)- q is 1 - p- E is the maximum error of estimate we allow, which is 6% or 0.06Using these values, we get:n = (2.58^2 * 0.5 * 0.5) / 0.06^2n ≈ 460.89Since we need a whole number for the sample size, we round up to the nearest integer:n = 461Therefore, we need to test 461 fish to be 99% confident that the true proportion of inedible fish is estimated to within 6%.

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