1. Stat 217 – Day 17
Review

2. Last Time – Confidence interval for m
Lab 2 – Goal is to estimate, on average, how long after the start of the party people tend to arrive.
Close to sample mean
Need to know how much sample mean might wander off, by random sampling chance alone, from the population mean (s/ )
Could also consider sample median

3. In general – Confidence interval
Quantitative or categorical data?
If categorical, can find a confidence interval for p
95% 2SD method: SE(p-hat)
One-sample z-interval
If quantitative, can find a confidence interval for m
95% 2SD method: SE(x-bar)
One-sample t-interval
Need to have decent sample size for these methods (e.g., 10S/10F or 20/normal)

4. Example 3.2 Calculating and interpreting a “one-sample z-interval”
“margin-of-error” = .014 or about 1.4 percentage points
Calculating and interpreting a “one-sample z-interval”
Observed sample proportion: 713/1034 = .69
√(.69*(1-.69)/1034)
(.676, .704)
I’m 95% confident that between 67.6% and 70.4% of the population will claim to have felt an impact from the Affordable Care Act
Assuming the sample was representative and no nonsampling errors

5. Body Temperatures Body temps for 130 healthy adults n = 130
Mean = F
s = F
Symmetric distribution

6. Body Temperatures
“margin-of-error” = .129 degrees
Calculating and interpreting a “one-sample t-interval”
Observed sample mean: degrees with sample standard deviation s = .733 degrees
ish (.733/sqrt(130))
(98.12, 98.38)
I’m 95% confident that the population mean healthy body temperature is between degrees and degrees Fahrenheit

7. Body Temperatures
Notice this interval is not very wide: It’s an interval for the population mean, not one person

8. Body Temperatures
Notice: This interval does not contain 98.6; we would not consider 98.6 to be a plausible value for the population mean body temperature
Of course, not terribly far away (98.12, 98.38)
Would still like to know more about how this sample was selected before deciding what population I think it is representative of

9. Section 3.4 Factors that impact width of confidence interval
Larger sample size  Narrower interval
Larger confidence level  Wider interval
(Proportion closer to 0.5  wider)
(Larger sample SD, s  wider)

10. Section 3.5
These confidence interval procedures only “work” if you have representative sample
Vs. voluntary response bias
Vs. bad sampling frame
and no “nonrandom” (nonsampling) errors
People change their minds
People don’t remember correctly
People lie/social expectation
Leading questions
Demeanor of interviewer

11. Gallup.com

12. Exam 1 May use one 8.5 x 11 (both sides) page of self-produced notes
Mixture of multiple choice, short answer, longer questions (see quizzes, labs, investigations)
Bring a calculator (not a cell phone)
Access to the computer (e.g., applets)
Probably a section of multiple choice questions on the computer

13. Exam 1 Resources Review handout Review questions/solutions
Chapters 0-3
Self-check videos, self-tests, what went wrong
Quiz solutions
Access to pre-labs
Grading comments on quizzes, investigations, labs

14. Exam 1 Advice Review handout, problems online Review labs
Work problems
Review labs
Start with ideas that we have emphasized more often
Be ready to interpret and explain

15. Some advice during exam
If you get stuck on a problem, move on
later parts, later problems
Try to hit the highlights in your answer (e.g., not all sources of bias, just the most serious)
Be succinct (think before you write)
Read the question carefully
Show all of your work, explain well
communication points, no “it”!
Read entire question before writing anything

16. Some big, big ideas Observational units, variable Probability
What see in sample (descriptive) vs. saying something beyond the sample (inferential)
Statistic vs. Parameter
Interpretation of p-value, Statistical significance
Estimation (confidence interval)
Generalizability
Interpretations, reasoning
Properties, “what if” questions…
How are you deciding this?

17. Main Topics
Sample from a random process (e.g., coin toss, dolphins, kissing couples)
Parameter: p = probability of “success”
Statistic: sample proportion
Random sample from a finite large population (e.g., Gallup poll)
Parameter: p = population proportion of “successes”
Statistic: sample proportion
Consider sampling, nonsampling biases

18. Previously
When have random sampling method, the mean of the “could have been” statistics will be equal to the population parameter
>> Will believe sample is representative of pop’n
The variability of the distribution of “could have been” statistics will decrease if you increase the sample size (number of observational units per sample)
Population size (assuming it’s pretty big to begin with) doesn’t really matter

19. Agree?

20. Main Topics
Sample from a random process or population with quantitative data
Parameter: m = population mean
Statistic: sample mean

21. Test of Significance Test a conjecture about parameter
Assume null hypothesis is true
Look at the random distribution of the statistic when the null hypothesis is true
Simulation (One Proportion applet)
Normal model (Theory Based Inference applet)
If observed value is in the tail of the distribution (small p-value, large z), reject the null hypothesis. Otherwise “fail to reject.”
FTR: Not convincing evidence against Ho

22. Test of Significance – Lab 2
Sample mean = 6.9 hours < 8 hours
The population mean is 8 hours and we just got an unlucky random sample
Small p-value discounts this explanation
Our sample is not representative of the population
Random sampling would discount this explanation
The population mean is actually less than 8 hours

23. Make sure you recognize
Interpreting the p-value vs. evaluating the p-value
3% of random samples … observed result … null hypothesis true
I find this p-value to be small so I reject the null hypothesis
Interpreting the confidence interval vs. the confidence level
I’m 95% confident that…this method … and .7323
If we took thousands of intervals, roughly 95% of the resulting intervals should contain the parameter

24. Confidence Interval Want to estimate parameter from the sample data
Could test all the possible values for parameter and make an interval of the ones that are not rejected
Not practical
Other ways to estimate a CI
estimate + 2 standard deviations
Get SD from simulation and/or from formula
Normal-based inference (TBI applet)
Larger sample sizes
Interpretation: I’m 95% confident that the parameter is between these two values
Procedure works 95% of the time

25. Questions? Optional Review Session Tonight Building 38, Room 219
Starting at 7:40