Question

You want to estimate the population mean by taking a sample and constructing a 80% confidence interval. You know the population standard deviation is 6.08. Compute the minimum sample size needed to ensure that your interval estimate has a margin of error less than or equal to 1.8.

Answer 1

Margin error = Z*(sigma/sqrt(n))

1.8= 1.285 (6.08/sqrt(n) (since z=1.285 for 80% C.I)

sqrt(n) = 7.8128/1.8

=4.34

This implies

n =(4.34)^2

n=18.83

n= 19