Confidence Interval (Place of Birth), Confidence Intervals | Statistics

Learning objectives

Confidence Interval (Place of Birth)

Student Learning Outcomes

The student will calculate the 90 percent confidence interval of the proportion of students in this school who were born in this state.
The student will interpret confidence intervals.
The student will determine the effects of changing conditions on the confidence interval.

Collect the Data

Survey the students in your class, asking them whether they were born in this state. Let X = the number who were born in this state.
1. n = ____________
2. x = ____________
In words, define the random variable P′.
State the estimated distribution to use.

Find the Confidence interval and Error bound

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 proportion.

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.

Describe the Confidence Interval

In two to three complete sentences, explain what a confidence interval means (in general), as though 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.
Construct a confidence interval for each confidence level given.

Confidence Level EBP/Error Bound Confidence Interval

50%

80%

95%

99%
What happens to the EBP 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	EBP/Error Bound	Confidence Interval
50%
80%
95%
99%