Question

A publisher wants to estimate the mean length of time​ (in minutes) all adults spend reading newspapers. To determine this​ estimate, the publisher takes a random sample of 15 people and obtains the results below. From past​ studies, the publisher assumes sigma is 2.1 minutes and that the population of times is normally distributed.

6 10 12 6 6 10 7 7 8 8 11 11 9 10 7

Construct the​ 90% and​ 99% confidence intervals for the population mean. Which interval is​ wider? If​ convenient, use technology to construct the confidence intervals.

The​ 90% confidence interval is ​( ____​, ____ ).​ (Round to one decimal place as​ needed.)

Answer 1

First we need to find the sample mean is:

Following is the screen shot of excel for 90% confidence interval:

Following is the output generated by excel:

Confidence interval - mean
	90%	confidence level
	8.53	mean
	2.1	std. dev.
	15	n
	1.645	z
	0.892	half-width
	9.422	upper confidence limit
	7.638	lower confidence limit

The 90% confidence interval is (7.6, 9.4).

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Following is the output generated by excel for 99% confidence interval:

Confidence interval - mean
	99%	confidence level
	8.53	mean
	2.1	std. dev.
	15	n
	2.576	z
	1.397	half-width
	9.927	upper confidence limit
	7.133	lower confidence limit

The 99% confidence interval is (7.1, 9.9).