Final answer:
To estimate the proportion of fishermen without a license, the game and fish commission needs to determine the minimum sample size to be 90% confident within a certain margin of error. Using the formula n = (Z^2 * p * (1-p)) / E^2, where Z is the z-score, p is the proportion estimate, and E is the margin of error, they can calculate the minimum sample size. In this case, the minimum sample size is 665.
Step-by-step explanation:
To estimate the proportion of fishermen fishing without a license, the game and fish commission needs to determine the minimum number of fishermen they must sample to be 90% confident that their estimate is within 0.025 of the population proportion. To do this, they can use the formula n = (Z^2 * p * (1-p)) / E^2, where Z is the z-score corresponding to the desired confidence level, p is an estimate of the proportion of fishermen without a license, and E is the desired margin of error. Since the proportion is unknown, they can use a conservative estimate of p = 0.5. Plugging in the values, the formula becomes n = (1.645^2 * 0.5 * (1-0.5)) / 0.025^2. Solving this equation gives a minimum sample size of 665.