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. Which interval is​ wider? If​ convenient, use technology to construct the confidence intervals.

A random sample of

3232

gas grills has a mean price of

​$642.50642.50.

Assume the population standard deviation is

​$59.1059.10.

the 90% confidence interval is??

the 95% confidence interval is??

which interval is wider?

Answer 1

Mean = 642.50

Sample size (n) = 32

Standard deviation (s) = 59.10

Confidence interval(in %) = 90

z @ 90.0% = 1.645

Since we know that

Required confidence interval

Required confidence interval = (642.5-17.1861, 642.5+17.1861)

Required confidence interval = (625.3139, 659.6861)

Confidence interval(in %) = 95

z @ 95.0% = 1.96

Since we know that

Required confidence interval

Required confidence interval = (642.5-20.4771, 642.5+20.4771)

Required confidence interval = (622.0229, 662.9771)

95% Confidence interval is wider than the 90%. Because z score is greater for 95% confidence interval.

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