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 $20.5 and the standard deviation is known to be $10.3 How large of a sample would be required in order to estimate the mean per capita income at the 85% level of confidence with an error of at most $0.43 Round your answer up to the next integer.

Answer 1

It is given that margin of error= 0.43 and standard deviation = 10.3

we need to find the sample size n with 85% confidence level

Using z distribution table, z critical value for 85% confidence level is 1.44

Using the sample size formula

setting the values, we get

(rounded to nearest whole number)

Therefore, required sample size n is 1190