Question

# Part of the population of 6,750 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 3 of them are infected. How many elk are likely to be infected?

Answer

Cannot determine how many elk are likely to be infected based on this sample alone.

- Calculate the proportion of infected elk in the sample. Let's call this p-hat. This is calculated by dividing the number of infected elk by the total sample size. p-hat = 3/50 = 0.06.
- Calculate the standard error of p-hat. This is calculated by taking the square root of p-hat times (1-p-hat) divided by the sample size, then multiplying by the z-score corresponding to the desired level of confidence. For a 95% level of confidence, the z-score is 1.96. SE(p-hat) = sqrt(0.06 * (1 - 0.06) / 50) * 1.96 = 0.086.
- Calculate the margin of error. This is calculated by multiplying the standard error by the z-score corresponding to the desired level of confidence. For a 95% level of confidence, the z-score is 1.96. ME = 0.086 * 1.96 = 0.169.
- Calculate the confidence interval. This is calculated by subtracting the margin of error from p-hat to get the lower bound, and adding the margin of error to p-hat to get the upper bound. CI = [0.06 - 0.169, 0.06 + 0.169] = [-0.109, 0.229]
- Because the lower bound is negative, we can conclude that there is not enough evidence to suggest that any elk are infected with the parasite. We cannot determine how many elk are likely to be infected based on this sample alone.