1. Stor 155, Section 2, Last Time Review…

2. Stat 31 Final Exam: Date & Time: Tuesday, May 8, 8:00-11:00 Last Office Hours: Thursday, May 3, 12:00 - 5:00 Monday, May 7, 10:00 - 5:00 & by email appointment (earlier) Bring with you, to exam: Single (8.5" x 11") sheet of formulas Front & Back OK

3. Review Slippery Issues Major Confusion: Population Quantities Vs. Sample Quantities

4. Levels of Probability Simple Events –Big Rules of Prob (Not, And, Or) –Bayes Rule Distributions (in general) –Defined by Tables Summary of discrete probs Get probs by summing –Uniform Get probs by finding areas

5. Levels of Probability Distributions (in general) Named (& Useful) Distributions –Binomial Discrete distribution of Counts Compute with BINOMDIST & Normal Approx. –Normal Continuous distribution of Averages Compute with NORMDIST & NORMINV –T Similar to Normal, for estimated s.d. Compute with TDIST & TINV

6. Today’s Focus Decisions you need to make While taking Final Exam When faced with a word problem Key to deciding on approach (knowing which formula to use)

7. Review Decisions Needed Main Challenge: Word problems on statistical inference Choices to keep in mind: 1.Big picture: a.Single Sample b.Two Samples c.Two Way Tables d.Regression

8. Review Decisions Needed 2.Probability model: a.Proportions – Counts (p based) b.Normal Means – Measurements (mu based)

9. Review Decisions Needed 2.Probability model: a.Proportions – Counts (p based) i.Best Guess ii.Conservative iii.BINOMDIST iv.Normal Approx to Binomial (used usually for Hypo tests, etc.)

10. Review Decisions Needed 2.Probability model: b.Normal Means (mu based) i.Sigma known – NORMDIST & NORMINV ii.Sigma unknown – TDIST & TINV

11. Review Decisions Needed 2.Probability model: (Keeping Excel functions straight) Cutoff → ProbProb → Cutoff Counts, Prop’nsBINOMDIST??? Meas. σ knownNORMDISTNORMINV Meas. σ unkno’nTDISTTINV

12. Review Decisions Needed 2.Probability model: (Keeping Excel functions straight) Recall horrible Excel Organizations Different functions work differently Indicate these on formula sheet…

13. Review Decisions Needed 2.Probability model: (Keeping Excel functions straight) What about ???: There is no BINOMINV Since tricky to invert discrete prob’s Have to use Normal Approx to Binomial

14. Review Decisions Needed 3.Inference Type: a.Confidence Interval b.Choice of Sample Size c.Hypothesis Testing (each has its set of formulas…)

15. Review Decisions Needed 3.Inference Type: a.Confidence Interval i.Binomial type: Best guess, NORMINV ii.Binomial type: Conservative, NORMINV iii.Normal, σ known: NORMINV or CONFIDENCE iv.Normal, σ unknown: TINV (each has its set of formulas…)

16. Review Decisions Needed 3.Inference Type: b.Choice of Sample Size i.Binomial type: Best guess, NORMINV ii.Binomial type: Conservative, NORMINV iii.Normal, σ known: NORMINV iv.Normal, σ unknown: TINV (each has its set of formulas…)

17. Review Decisions Needed 3.Inference Type: c.Hypothesis Testing – P-values i.Binomial type: NORMDIST (or BINOMDIST) ii.Normal, σ known: NORMDIST iii.Normal, σ unknown: TDIST iv.Variation, σ known: Z-stat v.Variation, σ unknown: t-stat (each has its set of formulas…)

18. Review Decisions Needed Summary of decisions 1. Big picture: (Single - Two Samples – 2 Way Tab’s – Reg’n) 2. Probability model: (Prop’ns (Counts) - Normal (Meas’ts)) 3. Inference Type: (Conf. Int. - Sample Size – Hypo Testing)

19. Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem Work that out (make decisions…) Mark it off Return & repeat Finish all correctly? An easy A in this course

20. And Now for Something Completely Different Einstein was once traveling from Princeton on a train when the conductor came down the aisle, punching the tickets of each passenger. When he came to Einstein, Einstein reached in his vest pocket. He couldn't find his ticket, so he reached in his other pocket.

21. And Now for Something Completely Different It wasn't there, so he looked in his briefcase but couldn't find it. Then he looked in the seat by him. He couldn't find it. The conductor said, "Dr. Einstein, I know who you are. We all know who you are. I'm sure you bought a ticket. Don't worry about it." Einstein nodded appreciatively.

22. And Now for Something Completely Different The conductor continued down the aisle punching tickets. As he was ready to move to the next car, he turned around and saw the great physicist down on his hands and knees looking under his seat for his ticket.

23. And Now for Something Completely Different The conductor rushed back and said, "Dr. Einstein, Dr. Einstein, don't worry. I know who you are. No problem. You don't need a ticket. I'm sure you bought one."

24. And Now for Something Completely Different Einstein looked at him and said, "Young man, I too know who I am. What I don't know is where I'm going."

25. A Request > Hi Professor Marron, > > For the review session, can we please go over the hypothesis testing and > when to use the one or two sided tests, and the overall process for > hypothesis testing? Thanks!!

26. Response 1.In review from April 19, did: (Hypo Testing: Pop’n vs. Sample) (So just do quick reminder here) 2.So here focus on 1-sided vs. 2-sided

27. Hypothesis Testing – Z scores E.g. Fast Food Menus: Test Using P-value = P{what saw or m.c.| H 0 & H A bd’ry} (guides where to put $21k & $20k)

28. Hypothesis Testing – Z scores P-value = P{what saw or or m.c.| H 0 & H A bd’ry}

29. Response 2.So here focus on 1-sided vs. 2-sided This was studied in detail on March 22, So review that But also consider Variations, i.e. how to twiddle problem to get opposite answer

30. Hypothesis Testing, III CAUTION: Read problem carefully to distinguish between: One-sided Hypotheses - like: Two-sided Hypotheses - like:

31. Hypothesis Testing Hints: Use 1-sided when see words like: –Smaller –Greater –In excess of Use 2-sided when see words like: –Equal –Different Always write down H 0 and H A –Since then easy to label “more conclusive” –And get partial credit….

32. Hypothesis Testing E.g. Text book problem 6.34: In each of the following situations, a significance test for a population mean, is called for. State the null hypothesis, H 0 and the alternative hypothesis, H A in each case….

33. Hypothesis Testing E.g. 6.34a An experiment is designed to measure the effect of a high soy diet on bone density of rats. Let = average bone density of high soy rats = average bone density of ordinary rats (since no question of “bigger” or “smaller”)

34. Variation E.g. 6.34a An experiment is designed to see if a high soy diet increases bone density of rats. Let = average bone density of high soy rats = average bone density of ordinary rats (since no question of “bigger” or “smaller”)

35. Hypothesis Testing E.g. 6.34b Student newspaper changed its format. In a random sample of readers, ask opinions on scale of -2 = “new format much worse”, -1 = “new format somewhat worse”, 0 = “about same”, +1 = “new a somewhat better”, +2 = “new much better”. Let = average opinion score

36. Hypothesis Testing E.g. 6.34b (cont.) No reason to choose one over other, so do two sided. Note: Use one sided if question is of form: “is the new format better?”

37. Hypothesis Testing E.g. 6.34c The examinations in a large history class are scaled after grading so that the mean score is 75. A teaching assistant thinks that his students have a higher average score than the class as a whole. His students can be considered as a sample from the population of all students he might teach, so he compares their score with 75. = average score for all students of this TA

38. Variation E.g. 6.34c The examinations in a large history class are scaled after grading so that the mean score is 75. A teaching assistant thinks that his students have a different average score from the class as a whole. His students can be considered as a sample from the population of all students he might teach, so he compares their score with 75. = average score for all students of this TA

39. Hypothesis Testing E.g. Textbook problem 6.36 Translate each of the following research questions into appropriate and Be sure to identify the parameters in each hypothesis (generally useful, so already did this above).

40. Hypothesis Testing E.g. 6.36a A researcher randomly divides 6-th graders into 2 groups for PE Class, and teached volleyball skills to both. She encourages Group A, but acts cool towards Group B. She hopes that encouragement will result in a higher mean test for group A. Let = mean test score for Group A = mean test score for Group B

41. Hypothesis Testing E.g. 6.36a Recall: Set up point to be proven as H A

42. Variation E.g. 6.36a A researcher randomly divides 6-th graders into 2 groups for PE Class, and teached volleyball skills to both. She encourages Group A, but acts cool towards Group B. She wonders whether encouragement will result in a different mean test for group A. Let = mean test score for Group A = mean test score for Group B

43. Variation E.g. 6.36a Recall: Set up point to be proven as H A

44. Hypothesis Testing E.g. 6.36b Researcher believes there is a positive correlation between GPA and esteem for students. To test this, she gathers GPA and esteem score data at a university. Let = correlation between GPS & esteem

45. Variation E.g. 6.36b Researcher investigates the potential correlation between GPA and esteem for students. To test this, she gathers GPA and esteem score data at a university. Let = correlation between GPS & esteem

46. Hypothesis Testing E.g. 6.36c A sociologist asks a sample of students which subject they like best. She suspects a higher percentage of females, than males, will name English. Let: = prop’n of Females preferring English = prop’n of Males preferring English

47. Variation E.g. 6.36c A sociologist asks a sample of students which subject they like best. Is there a difference between the percentage of females & males, that name English. Let: = prop’n of Females preferring English = prop’n of Males preferring English