1. Chapter 8: Estimating With Confidence
What is a confidence interval?

2. Statistical Inference:
Using sample data to draw conclusions about a population
Note:
Each sample may vary, but the population parameter doesn’t!
Point Estimator – a statistic that provides an estimate of a population parameter
Example: Estimate the percent (proportion) of time a Hershey’s kiss will land on its base when dropped

3. Confidence Interval:
Uses the sample distribution to predict population parameter
It is an interval of numbers above and below the sample statistic
Example: “I am 95% confident that the interval 45% to 55% captures the true percentage of Harrison students that did all of their homework last night.

4. Confidence Level:
The probability the interval will capture the true parameter value in repeated samples – 90% or higher
Critical Value:
The value that has the probability p lying to its right under the standard Normal curve. ( Z* )

5. Margin of Error:
How accurate our estimate is based on the variability of the sample distribution. We add and subtract this from our estimate.
estimate  margin of error
Caution: Margin of error is only from random sampling errors. This does not include errors in collecting the data!

6. Most Common Critical Values
Confidence Level (C) Upper tail prob. Z* Value
90%
 1.645
0.05
0.90
0.05
0.05
Z=?
Z=?

8. Most Common Critical Values
Confidence Level (C) Upper tail prob. Z* Value
95%
 1.96
0.025
0.95
0.0255
0.025
Z=?
Z=?

9. Most Common Critical Values
Confidence Level (C) Upper tail prob. Z* Value
99%
 2.576
0.005
0.005
0.99
0.005
0.005
Z=?
Z=?

10. Interpreting a Confidence Interval:
What you will say:
I am C% confident that interval _______ to ________ captures the true parameter.
What it means:
If we took many, many SRS from a population and calculated a confidence interval for each sample, C% of the confidence intervals will contain the true parameter.

11. CAUTION!
Never Say:
The interval will capture the true mean C% of the time.
It either does or does not!

12. Steps to Construct ANY Confidence Interval:
PANIC P:
Parameter of Interest (what are you looking for?) A:
Assumptions (what are the conditions?) N:
Name the type of interval (what type of data do we have?) I:
Interval (Finally! You can calculate!) C:
Conclusion in context (I am ___% confident the interval ______ to _______ captures the true parameter (in context).