1. Introduction to Inference
Confidence Intervals
Significance Test
Use and Abuse of Statistical Inference
*Grab your computer (same # as your calculator) and log in. We’ll use them briefly today

2. Hershey Kisses- Do this at beginning of unit

3. Hershey Kisses- Do this at beginning of unit

4.
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

5.
#4)…if a sample of 25 candies from the machine contained 10 orange candies…
#6) …(that’s 40% orange)? How about 10 orange candies (20% orange)? Explain

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

8. 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….

9. Vocab
Statistical inference- drawing conclusions about population based on data from sample
Parameters- #s that describe population
Statistic- # calculated from sample

10. What is our population? Parameter? Statistic?
The 2007 Youth Risk Behavior Survey questioned 14,041 students grades Of these 2808 said they had smoked cigarettes at least one day in the past month. That’s 20.0% of the sample.
What is our population? Parameter? Statistic?
A basic strategy in stat inference is to use sample statistic to est a population parameter. We est the parameter as “about 20.0%”. We can only est that the true population parameter is that. A 95% confidence interval makes that “about” precise.

11. Hershey Kiss Finish the worksheet- 10 minutes
The true proportion of Hershey kisses that land on their base is .33
Determine if your interval captures the true proportion
Write your interval on either green or pink paper (green= interval does capture, pink=interval does not capture)
Tape your paper to the board

12. Critical Values
Find Z* for
90%
85%
92%

13. Demo of CI in Price is Right (sort of)

15. 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

16. 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.

17. 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

18. One-Sample z-interval for a Population Proportion
The approximate conf int for p is

19. 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

22. Create a 90% and 99% confidence interval for the
proportion of red beads in the jar using your sample

24. Recap of Confidence Intervals
To estimate a parameter:
1) Determine what you are measuring
2) Check the conditions
3) Create a confidence interval (this gives you the plausible values)

26. Suppose a SRS of 358 beads results in 135 red beads.
Using sample results to estimate p
Suppose a SRS of 358 beads results in 135 red beads.
This is a point estimate for p

27. 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%.

28. Globe Activity
What % of the time do we land on water with our left thumb?
Check conditions
Construct a 96% confidence interval
Throw the ball to students, count if their thumb is on water/total
For hyp testing– test if globe is made correctly by comparing to the actual percent of real world that is covered in water (71%).

30. 200 Test Scores
Finding the confidence interval for the mean of these test scores. The population standard deviation is 13.2.
Pick 30 numbers and find the mean of them
Check the conditions
Calculate a 90% confidence interval
Calculate a 95% confidence interval

31. 200 Test Scores
The true population mean is If your interval captures the mean, write on green paper. If your interval does not capture the mean, write on pink paper. 6. Tape both intervals in the appropriate spot on the board

32. Example 1 (BVD3e p. 530)
To check adherence to the speed limit on a particular stretch of road the speed was recorded for a random sample of 37 vehicles. The average was mph with a standard deviation of 5.01 mph.

33. Example 2 (BVD3e p. 558)
How far does a pro drive the golf ball? To estimate this, a random sample of 63 distances was recorded with a mean of yards and a standard deviation of 9.31 yards.

34. Using One-Sample t Procedures:
The Normal Condition
• Large Samples: The t procedures can be used even for clearly skewed distributions when the sample is large, roughly n ≥ 30
• Small samples: Use t procedures if the data appear close to Normal (roughly symmetric, single peak, no outliers). If the data are clearly skewed or if outliers are present, do not use t.

35. Example 3 (BVD3e p. 558)
In 1998 Nabisco Foods advertised that each 18-oz bag of Chips Ahoy cookies contained at least 1000 chocolate chips. Air Force Academy statistics students purchased randomly selected bags of cookies and counted the chocolate chips.

36. Example 3 (BVD3e p. 558)
1219
1214
1087
1200
1419
1121
1325
1345
1244
1258
1356
1132
1191
1270
1295
1135

37. Example 4 (BVD3e p. 558)
A researcher tests a maze on several rats, collecting time to complete in minutes.
38.4
46.2
62.5
38.0
62.8
33.9
50.4
35.0
52.8
60.1
55.1
57.6
55.5
49.5
40.9
44.3
93.8
47.9
69.2