Question

An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is 21.5, and the variance is known to be30.25. How large of a sample would be required in order to estimate the mean per capita income at the 98

Answer 1

To estimate the mean per capita income for a major city in Texas at 98% confidence level, we can use the formula n = (Z^2 * σ^2) / E^2.

Step-by-step explanation:

To estimate the mean per capita income for a major city in Texas with a confidence level of 98%, we need to determine the required sample size. We have the variance, which is known to be 30.25.

To calculate the sample size, we can use the formula:

n = (Z^2 * σ^2) / E^2

Where:

• n = required sample size
• Z = Z-score corresponding to the desired confidence level (e.g., for 98% confidence, Z = 2.33)
• σ^2 = known variance
• E = maximum error (desired precision)

Substituting the given values into the formula, we have:

n = (2.33^2 * 30.25) / E^2

To determine the value of E (maximum error), we need to specify the desired precision or margin of error. Once we have that value, we can calculate the required sample size using the formula above.