Final answer:
To estimate a population proportion with a 90% confidence level and a 2.5% margin of error, when the population proportion is believed to be 38%, we can use the sample size formula and plug in the values to calculate the required sample size.
Step-by-step explanation:
In this scenario, we are dealing with sample size determination to estimate a population proportion with a given level of confidence and margin of error. To find out the required sample size, we use the formula for calculating the sample size for a proportion, which is: n = (Z^2 * p * (1-p)) / E^2. Here, n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated population proportion, and E is the margin of error.
Let's plug in the values: Z is 1.645 for 90% confidence (from Z-table), p is 0.38 (38%), and E is 0.025 (2.5%). Plugging these values into the formula, we get the required sample size.
To perform the calculation: n = (1.645^2 * 0.38 * (1-0.38)) / 0.025^2. After calculating, be sure to round up to the next whole number, as we cannot survey a fraction of a person.