Question

What sample size is required to estimate the proportion of people with blood type O in a population of 1500 people to be within 0.02 of the true proportion with 95\% confidence? Assume no prior knowledge about the proportion. 4. For the population of Exercise 3, what sample size is required to simultaneously estimate the proportion with each blood type to within 0.02 of the true proportion with 95% confidence?

Answer 1

To estimate the proportion of people with blood type O in a population of 1500 to be within 0.02 of the true proportion with 95% confidence, a sample size of 9604 is required.

Step-by-step explanation:

To estimate the proportion of people with blood type O in a population of 1500 to be within 0.02 of the true proportion with 95% confidence, we can use the formula:

n = (Z^2 * p * (1-p)) / E^2

where n is the sample size, Z is the Z-score for the desired confidence level (Z = 1.96 for 95% confidence), p is the estimated proportion (since we have no prior knowledge, assume p = 0.5 for worst-case scenario), and E is the margin of error (E = 0.02).

Substituting the values into the formula:

n = (1.96^2 * 0.5 * (1-0.5)) / 0.02^2

n = 9604

Therefore, a sample size of 9604 would be required to estimate the proportion of people with blood type O to within 0.02 with 95% confidence.