Question

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals.

A random sample of 40 home theater systems has a mean price of ​$140.00 Assume the population standard deviation is ​$19.50.

The 90% confidence interval is?

The 95% confidence interval is?

Answer 1

n= 40, = 140, = 19.50

We are using TI-83 calculator as folllows,

a)

c= 90 %

134.93 < < 145.07

The​ 90% confidence interval is ( 134.93 , 145.07)

b)

c= 95 %

133.96 < < 146.04

The​ 95% confidence interval is ( 133.96 , 146.04)

c)

With​ 90% confidence, it can be said that the population mean price lies in the first interval. With​ 95% confidence, it can be said that the population mean price lies in the second interval. The​ 95% confidence interval is wider than the​ 90%.