Question

A simple random sample of 60 items from a population with σ = 8 resulted in a sample mean of 32. (Round your answers to two decimal places.) (a) Provide a 90% confidence interval for the population mean. to (b) Provide a 95% confidence interval for the population mean. to (c) Provide a 99% confidence interval for the population mean. to

Answer 1

a) From standard normal tables, we have:
P(-1.645 < Z < 1.645) = 0.9

Therefore the confidence interval here is obtained as:

This is the required 90% confidence interval here.

b) From standard normal tables, we have:
P(-1.96 < Z < 1.96) = 0.95

Therefore the confidence interval here is obtained as:

This is the required 95% confidence interval here.

c) From standard normal tables, we have:
P(-2.576 < Z < 2.576) = 0.99

Therefore the confidence interval here is obtained as:

This is the required 99% confidence interval here.