Confidence Interval (Home Costs), Confidence Intervals | Statistics

Learning objectives

Confidence Interval (Home Costs)

Student Learning Outcomes

The student will calculate the 90 percent confidence interval for the mean cost of a home in the area in which this school is located.
The student will interpret confidence intervals.
The student will determine the effects of changing conditions on the confidence interval.

Collect the Data

Check the Real Estate section in your local newspaper. Record the sale prices for 35 randomly selected homes recently listed in the county.

Complete the following table:

__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________

Describe the Data

Compute the following:
1. $\bar{x}$ = _____
2. $s_{x}$ = _____
3. n = _____
In words, define the random variable $\bar{X}$ .
State the estimated distribution to use. Use both words and symbols.

Find the Confidence interval

Calculate the confidence interval and the error bound.
1. Confidence interval: _____
2. Error Bound: _____
How much area is in both tails (combined)? α = _____
How much area is in each tail? $\frac{α}{2}$ = _____
Fill in the blanks on the graph with the area in each section. Then, fill in the number line with the upper and lower limits of the confidence interval and the sample mean.
View original figure (external; image not reproduced in this text edition)
Original figure description: Normal distribution curve with two vertical upward lines from the x-axis to the curve. The confidence interval is between these two lines. The residual areas are on either side.
Some students think that a 90 percent confidence interval contains 90 percent of the data. Use the list of data on the first page and count how many of the data values lie within the confidence interval. What percentage is this? Is this percentage close to 90 percent? Explain why this percentage should or should not be close to 90 percent.

Describe the Confidence Interval

In two to three complete sentences, explain what a confidence interval means (in general), as if you were talking to someone who has not taken statistics.
In one to two complete sentences, explain what this confidence interval means for this particular study.

Use the Data to Construct Confidence Intervals

Using the given information, construct a confidence interval for each confidence level given.

Confidence Level EBM/Error Bound Confidence Interval

50%

80%

95%

99%
What happens to the EBM as the confidence level increases? Does the width of the confidence interval increase or decrease? Explain why this happens.

Attribution. Statistics, OpenStax, Rice University, and the contributing authors credited in the book. Licensed under Creative Commons Attribution 4.0 International. Source revision 7dea80ae28 of openstax/osbooks-statistics (2026-04-23). CC BY 4.0. Original source ↗. Text edition of a pinned CC BY 4.0 source revision of the OpenStax book, converted from CNXML by the EvidenceHelix importer. Original prose, learning objectives, tables, exercises, glossary and captions are preserved; images are not copied (figures link to the original source and keep their credits). No new content was added. Later revisions of this book can carry different licence terms and are not used.

Confidence Level	EBM/Error Bound	Confidence Interval
50%
80%
95%
99%