Question

Mean Income of NYC Household Heads: Suppose researchers want to conduct a study on the mean income of NYC household heads. From previous studies they know that the standard deviation in the population is approximately $30,000. 1) How large should a simple random sample be to estimate mean income with a standard error of $1,000? Show all main steps of your calculation. (No points will be given to an answer of only a final number provided even if the number is correct.) 2) How large should a simple random sample be to estimate mean income with a margin of error of at most $2,000 and a confidence level of 95%? Please use 1.96 (not 2) for the critical value z. Show all main steps of your calculation. (No points will be given to an answer of only a final number provided even if the number is correct.)

Answer 1

1. Here we are given that standard error=1000 and standard deviation=30000

Now standard error is (standard deviation)/sqrt(n)

So sqrt(n)=sd/se=30000/1000=30

So n=900

2. Here E=2000 and z=1.96

So