1. CONFIDENCE INTERVALS What is the Purpose of a Confidence Interval?
How are Confidence Intervals Different from Tests of Significance?
How Do Confidence Intervals Work?
What Determines the Width of a Confidence Interval?
What is Margin of Error?

2. What is the Purpose of a Confidence Interval?
Estimate a range of values thought to contain a population parameter (e.g., mean) with a certain level of confidence (e.g., 95%).
Focus is on estimating, not testing a hypothesis.

3. How Are Confidence Intervals Different From Tests of Significance?
Significance tests test a hypothesis while confidence intervals estimate.
Confidence intervals are interval estimates rather than point estimates. Interval estimates are less precise than point estimates but more likely to be correct.

4. How Do Confidence Intervals Work?
Confidence Interval for the Mean with z-Scores
Confidence Interval for the Mean with t-scores
Confidence Interval for the Proportion

5. Confidence Interval for the Mean with z- scores
Provide a range of values to estimate the population mean.
Use when the population standard deviation is known.
Assumptions are the same as for a z-Test.

6. How it Works
Start with your sample mean as the middle of the interval.
Establish upper and lower limits depending on how confident you want to be.
Determine the upper and lower limits using z-scores from the normal distribution, e.g. 95% confidence corresponds to z-scores of and

7. lower limit
upper limit M

8. Confidence Interval for the Mean with t- scores
Provide a range of values to estimate the population mean.
Use when the population standard deviation is not known but can be estimated from the sample standard deviation.
Assumptions are the same as for a single-sample t-test.

9. Confidence Interval for a Proportion
Provide a range of values thought to contain the population proportion or percentage.
Often used with survey results.
Must have independent observations and a representative sample.

10. Confidence Interval for a Proportion
Use z-scores to establish limits.
Use standard error of proportion instead of standard error of mean.
Standard error of proportion is based on sample size and proportion of interest (larger standard error when proportion is closer to .50).

11. What Determines the Width of a Confidence Interval?
A narrower interval is more informative.
The interval will be narrower with
a larger sample
lower variability
a lower level of confidence

12. What is Margin of Error?
The margin of error is the quantity added and subtracted to the point estimate to get the upper and lower limits.
Media reports of survey results usually include margin of error (the +/- part).

13. What is Margin of Error?
Can be used as an indirect test of significance
Construct confidence interval around sample statistic using margin of error
If interval includes Ho value, difference is not significant