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%?

Question

Quizplus · Accepted Answer

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 0.06

Using these values, we get:
n = (2.58^2 * 0.5 * 0.5) / 0.06^2
n ≈ 460.89

Since we need a whole number for the sample size, we round up to the nearest integer:
n = 461

Therefore, we need to test 461 fish to be 99% confident that the true proportion of inedible fish is estimated to within 6%.

A Researcher Wishes to Estimate the Proportion of Fish in a Certain