# Lesson 10: Confidence Intervals

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### Assignments

• Read Chapters 20 and 21 (sections 21.1 and 21.2 only) in the text.
• Work through the Lesson 10 online notes that follow.
• Complete all lesson assignments as listed in the Canvas Module.

### Learning Objectives

#### Chapters 20 and 21

After successfully completing this lesson, you should be able to:

• Interpret confidence intervals for population values.
• Find confidence intervals for population proportions and means using random samples.
• Understand the key principles of estimation:
1. Confidence intervals are random quantities, varying from sample to sample.  Sometimes these random intervals cover the true population parameter and sometimes they don't.  The coverage probability (the chance that the interval covers the parameter) is called the confidence level.
2. There is a trade-off between confidence and reliability.  In order to achieve a higher level of confidence, you must be willing to accept a larger margin of error (a wider interval) or pay the price of a larger sample size.
3. The variability of a sample statistic decreases with the square root of the sample size.  For example, when the sample size is four times as large, the margin of error will be cut in half.
4. Formulas for making confidence intervals are based on the probabilities associated with the randomization used to collect the data.
• Apply appropriate decision rules to determine whether or not there is a statistically significant difference between two population values.

### Terms to Know

#### From Chapter 20

• population value
• population proportion
• sample proportion
• categorical data
• confidence interval
• confidence level
• multiplier number
• standard error of a sample proportion
• margin of error

#### From Chapter 21

• population mean
• sample mean
• standard error of a sample mean (S.E.M.)
• population mean difference
• sample mean difference