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%.**

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