We draw a random sample of size 36 from a population with th

We draw a random sample of size 36 from a population with the standard deviation 3.5. If the sample mean is 27, what is a 95% confidence interval for the population mean?

A. [25.8567, 28.1433]

B. [26.0405, 27.9595]

C. [26.8100, 27.1900]

D. [26.8401, 27.1599]

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

xbar - Z*s/vn = 27 -1.96*3.5/sqrt(36) =25.85667

So the upper bound is

xbar +Z*s/vn =27 +1.96*3.5/sqrt(36) =28.14333

Answer: A. [25.8567, 28.1433]