1. New Year! Fresh Start (sort of…)
Stop doing
Continue doing
Start doing

2. Unit 8: Estimating with Confidence
8.1
Confidence Intervals
(The Basics)

3. Understand confidence interval Interpret confidence level
Objectives:
Understand confidence interval
Interpret confidence level
and confidence interval
Construct a Conf Int
Use Conf Int under the appropriate conditions
Emphasize the appearance of “and confidence interval” b\c there is a huge difference between the two parts of this objective.
Let students know that the conditions required to use a ConfInt should be familiar.

4. A single value produced by your estimator
Point Estimator
A statistic that provides an estimate of some population parameter using a sample
Point Estimate
A single value produced by your estimator
Remind students of German Tanks simulation and how each of them invented an estimator.
When def for Pt. Est. comes up add in the idea of “best guess” but clearly a long-shot to be absolutely on target!

5. What makes a good estimator? Unbiased 𝒑 and 𝒙 (so far) Low Variability
Recall:
What makes a good estimator?
Unbiased
𝒑 and 𝒙 (so far)
Low Variability
Sample size!
Write on the board how p-hat and x-bar are calculated, just to remind students.
Recall that increasing the sample size always decreases variability of the sampling distribution, but we also want a particular shape…

6. Recall Penny Ages Applet: Population mean: 12.26 yrs
Population stdev: yrs
Grab the poster of the sampl. distr. of x-bar when n=49 and remind them that this sampl. distr. had low variability (spread) and is approx norm (shape) b/c n > 30. See if you can elicit a recall of when you get and emphasize that these are approx % for 1sigma-2sigma-3sigma Then go out 2sigma (of the sampl distr NOT the pop) and count the number of dots within that 2sigma

7. Confidence Interval for a population parameter: Interval Itself:
pt.est. ± margin of error
Confidence Level C:
Success rate of the method in repeated sampling
Link plausible-reasonable-likely

8.
Go to website and run 95% confidence with a few samples, one at a time, so that stu see ConfInt created. Show them the point and the ME. Then do 50 at a time…note the running % of those CIs which capture the true pop parameter

9. This is a screen shot, just in case the website doesn’t work.

11. Observations about applet: The center of each interval is the pt.est.
The dist. from pt.est. to either end of the interval is the margin of error
IF we created EVERY interval poss. then ______% of the intervals would contain pop. parameter
Give examples of intervals and have students identify the pt. est. and the ME. The blank in bullet 3 is predetermined when we declare how confident we wish to be….

12. A set of plausible values for the pop. parameter
Interpreting!!
Confidence Level
How likely is our method to produce an interval that captures a parameter if we use it many times?
Confidence Interval
A set of plausible values for the pop. parameter
Give examples of intervals and have students appropriately interpret both the interval and the confidence level.

13.
Back to website & show how intervals change when conf level changes. What would it take to be 100% confident?

14. Our confidence level and the type of statistic determines this value
Constructing a Con Int
pt. est. ± margin of error
statistic ± (crit value)(stdev of stat)
Our confidence level and the type of statistic determines this value

15. Normal (b/c sample size is large enough)
Conditions for constructing a confidence interval:
Random
Independent
Normal (b/c sample size is large enough)
Random: SRS
Indep: 10n < N
Normal: p-hat vs. x-bar

16. Example:
In a survey, researchers asked adults aged 35 to 50 years if they used social media. A 90% confidence interval was calculated as being 73%, plus/minus 2.35%.