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 $18.1, and the variance is known to be $72.25.

How large of a sample would be required in order to estimate the mean per capita income at the 80% level of confidence with an error of at most $ 0.54?

Answer 1

To estimate the mean per capita income for a major city in Texas at the 80% level of confidence with an error of at most $0.54, the required sample size is approximately 43.

Step-by-step explanation:

To estimate the mean per capita income for a major city in Texas at the 80% level of confidence with an error of at most $0.54, we need to determine the required sample size.

1. First, we need to find the critical value associated with a confidence level of 80%. This can be done using a standard normal distribution table or calculator, which gives us a critical value of approximately 1.282.
2. Next, we can use the formula for sample size calculation: n = (z * σ) / E where 'n' is the required sample size, 'z' is the critical value, σ is the population standard deviation, and 'E' is the maximum error.
3. Plugging in the values, we have n = (1.282 * √72.25) / 0.54. Solving this equation gives us a required sample size of approximately 43.

Therefore, the economist would need a sample size of at least 43 in order to estimate the mean per capita income with an 80% confidence level and an error of at most $0.54.