1. What Is a Confidence Interval Anyway?

2. Definitions Confidence: firm belief, trust, reliance
Interval: the set containing all numbers between two given numbers and including one, or both, endpoints

3. What Do We Trust The interval?
The method used to produce the interval?

4. Central Limit Theorem Basis of our firm belief and trust
Shape of Sampling Distribution of Sample Means

5. Properties of Distribution
Mean
Standard Deviation

6. Before Sampling
Probability that sampling method will produce a sample mean within z standard deviations of the MEAN.
Amount of error that is acceptable?

7. Calculation of Error Error =
Margin of error in a confidence interval covers only random sampling errors

8. Reminder: no sample yet
Will our sample produce a sample mean that is in this interval?
What proportion of all samples will produce a sample mean in this interval?
What is the probability that our sample will produce a sample mean in this interval?
Reminder: no sample yet

9. After Sampling
Sample mean is on the horizontal axis of sampling distribution
Where is it?

10. Is Our Sample Mean In

11. Sample Mean
In the interval.
So what?
Not in the interval.

12. Interval of Plausible Parameters for which statistic is likely to occur

14. in

15. Confidence?
Question of probability?
What exactly are we confident of?

16. What Is a Confidence Interval Anyway?
An interval that may or may not contain
When will the interval contain ?
An interval that gives us a range of plausible values of
An interval that has probability of 0 or 1of actually containing

17. Statement
With ____% confidence, I believe to lie within the interval calculated.
Therefore I am ___% confident that this interval contains