Answer:
Population standard deviation Š± =1000
95% confidence interval width should not be more than $100.
Hence, (x+E) - (x-E) ā¤ 100
2E ā¤ 100
E ā¤ 100/2
E ā¤ 50
Level of significance is ā = 0.05 . Using the normal area table values at 0.05, the critical value is Z(ā/2) = 1.96
Computation of the sample size required.
n = [ (Z(ā/2) * Š±) / E]^2
n = [1.96 Ā * 1000 / 50]^2
n = 39.2^2
n = 1536.64
n = 1537
Hence, the economist needed a sample size of 1537 for a 95% confidence interval if the width of the interval should not be more than $100.
