2. Modern Languages 14131211109 87 6 54321 111098765 43 2 Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 212019181716 1514 13 12111098 212019181716 13 12111098 141312 table 7 6 54321 Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 321 21 1413 Projection Booth 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 7 6 5432 1 765 43 2 1 7 6 5432 1 765 43 2 1 7 6 54321 765 43 2 1 7 6 54321 765 43 2 1 7 6 54321 table Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 321 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 282726 2524 23 22 R/L handed broken desk Stage Lecturer’s desk Screen 1

3. MGMT 276: Statistical Inference in Management Spring 2015

5. Before our next exam (March 24 th ) Lind (5 – 11) Chapter 5: Survey of Probability Concepts Chapter 6: Discrete Probability Distributions Chapter 7: Continuous Probability Distributions Chapter 8: Sampling Methods and CLT Chapter 9: Estimation and Confidence Interval Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Plous (10, 11, 12 & 14) Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness Schedule of readings

6. By the end of lecture today 3/10/15 Use this as your study guide Confidence Intervals Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) what does p < 0.05 mean? what does p < 0.01 mean? One-tail versus Two-tail test Type I versus Type II Errors

7. Exam 2 –Tuesday March 24 th Study guide is online Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID Stats Review by Jonathon & Nick When: Monday evening March 23 rd 7:30 – 9:30pm (Immediately following Accounting review) McClelland Hall 207 (Berger Hall) Cost: $5.00 Stats Review by Jonathon & Nick When: Monday evening March 23 rd 7:30 – 9:30pm (Immediately following Accounting review) McClelland Hall 207 (Berger Hall) Cost: $5.00

8. No Homework Just study for exam

9. Have a safe and happy spring break No class on Thursday.

10. Review of Homework Worksheet just in case of questions

11. Confidence interval uses SEM

12. z scores for different levels of confidence Level of Alpha 1.96 =.05 2.58 =.01 1.64 =.10 90% How do we know which z score to use?

13. Upper boundary raw score x = mean + (z)(standard deviation) x = 55 + (+ 2.58)(10) x = 80.8 Lower boundary raw score x = mean + (z)(standard deviation) x = 55 + (- 2.58)(10) x = 29.2 29.2 80.8 29.2 80.8

14. Upper boundary raw score x = mean + (z)(standard error mean) x = 55 + (+ 2.58)(1.42) x = 58.7 Lower boundary raw score x = mean + (z)(standard error mean) x = 55 + (- 2.58)(1.42) x = 51.3 29.2 80.8 51.3 58.7 10 49 1.42 51.3 58.7

15. 29.2 80.8 58.7 8.02 8.6 9.18 7.8 8.6 9.4 51.3 10.2 29.8 23.1 16.9 4.09 13.11 9.18 8.02 2.67 14.5 9.4 7.8

16. Confidence Interval of 99% Has and alpha of 1% α =.01 Confidence Interval of 90% Has and alpha of 10% α =. 10 Confidence Interval of 95% Has and alpha of 5% α =.05 99%95%90% Area outside confidence interval is alpha Area in the tails is called alpha Area associated with most extreme scores is called alpha Critical z -2.58 Critical z 2.58 Critical z -1.96 Critical z 1.96 Critical z -1.64 Critical z 1.64

17. Rejecting the null hypothesis The result is “statistically significant” if: the observed statistic is larger than the critical statistic observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x 2 ) to be big!! the p value is less than 0.05 (which is our alpha) p < 0.05 If we want to reject the null, we want our “p” to be small!! we reject the null hypothesis then we have support for our alternative hypothesis A note on decision making following procedure versus being right relative to the “TRUTH”

18. . Decision making: Procedures versus outcome Best guess versus “truth” What does it mean to be correct? Why do we say: “innocent until proven guilty” “not guilty” rather than “innocent” Is it possible we got a verdict wrong?

19. .. We make decisions at Security Check Points

20. .. Type I or Type II error? Does this airline passenger have a snow globe? Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!! As detectives, do we accuse her of brandishing a snow globe?

21. . Decision made by experimenter Status of Null Hypothesis (actually, via magic truth-line) Reject H o “yes snow globe, stop!” Do not reject H o “no snow globe move on” True H o No snow globe False H o Yes snow globe You are right! Correct decision You are wrong! Type I error (false alarm) You are right! Correct decision You are wrong! Type II error (miss) Are we correct or have we made a Type I or Type II error? Does this airline passenger have a snow globe? Note: Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!!

22. . Type I or type II error? Does this airline passenger have a snow globe? Type I error: Rejecting a true null hypothesis Saying the she does have snow globe when in fact she does not (false alarm) Type II error: Not rejecting a false null hypothesis Saying she does not have snow globe when in fact she does (miss) What would null hypothesis be? This passenger does not have any snow globe Two ways to be correct: Say she does have snow globe when she does have snow globe Say she doesn’t have any when she doesn’t have any Two ways to be incorrect: Say she does when she doesn’t (false alarm) Say she does not have any when she does (miss) Which is worse? Decision made by experimenter Reject H o Do not Reject H o True H o False H o You are right! Correct decision You are wrong! Type I error (false alarm) You are right! Correct decision You are wrong! Type II error (miss)

23. . Type I or type II error Does advertising affect sales? Type I error: Rejecting a true null hypothesis Saying the advertising would help sales, when it really wouldn’t help people (false alarm) Type II error: Not rejecting a false null hypothesis Saying the advertising would not help when in fact it would (miss) What would null hypothesis be? This new advertising has no effect on sales Two ways to be correct: Say it helps when it does Say it does not help when it doesn’t help Two ways to be incorrect: Say it helps when it doesn’t Say it does not help when it does Which is worse? Decision made by experimenter Reject H o Do not Reject H o True H o False H o You are right! Correct decision You are wrong! Type I error (false alarm) You are right! Correct decision You are wrong! Type II error (miss)

24. . What is worse a type I or type II error? What if we were looking at a new HIV drug that had no unpleasant side affects Type I error: Rejecting a true null hypothesis Saying the drug would help people, when it really wouldn’t help people (false alarm) Type II error: Not rejecting a false null hypothesis Saying the drug would not help when in fact it would (miss) What would null hypothesis be? This new drug has no effect on HIV Two ways to be correct: Say it helps when it does Say it does not help when it doesn’t help Two ways to be incorrect: Say it helps when it doesn’t Say it does not help when it does Which is worse? Decision made by experimenter Reject H o Do not Reject H o True H o False H o You are right! Correct decision You are wrong! Type I error (false alarm) You are right! Correct decision You are wrong! Type II error (miss)

25. . Type I or type II error What if we were looking to see if there is a fire burning in an apartment building full of cute puppies Type I error: Rejecting a true null hypothesis (false alarm) Type II error: Not rejecting a false null hypothesis (miss) What would null hypothesis be? No fire is occurring Two ways to be correct: Say “fire” when it’s really there Say “no fire” when there isn’t one Two ways to be incorrect: Say “fire” when there’s no fire (false alarm) Say “no fire” when there is one (miss) Which is worse?

26. . Type I or type II error What if we were looking to see if an individual were guilty of a crime? Type I error: Rejecting a true null hypothesis Saying the person is guilty when they are not (false alarm) Sending an innocent person to jail (& guilty person to stays free) Type II error: Not rejecting a false null hypothesis Saying the person in innocent when they are guilty (miss) Allowing a guilty person to stay free What would null hypothesis be? This person is innocent - there is no crime here Two ways to be correct: Say they are guilty when they are guilty Say they are not guilty when they are innocent Two ways to be incorrect: Say they are guilty when they are not Say they are not guilty when they are Which is worse?

27. Rejecting the null hypothesis The result is “statistically significant” if: the observed statistic is larger than the critical statistic (which can be a ‘z” or “t” or “r” or “F” or x 2 ) observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x 2 ) to be big!! the p value is less than 0.05 (which is our alpha) p < 0.05 If we want to reject the null, we want our “p” to be small!! we reject the null hypothesis then we have support for our alternative hypothesis

28. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = 2.0? Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference Not a Significant difference

29. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = 1.5? Do Not Reject the null Do Not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels Not a Significant difference

30. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = -3.9? Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference p < 0.01 Yes, Significant difference

31. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = -2.52? Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference Not a Significant difference

32. z score = 1.64 One versus two tail test of significance: Comparing different critical scores (but same alpha level – e.g. alpha = 5%) One versus two tailed test of significance How would the critical z change? Pros and cons… 5% 95% 2.5% 95% 2.5%

33. One versus two tail test of significance 5% versus 1% alpha levels -1.64 or +1.64 How would the critical z change? One-tailedTwo-tailed α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 5% 2.5% 1%.5%

34. -1.64 or +1.64 How would the critical z change? One-tailedTwo-tailed α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 What if our observed z = 2.0? Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z One versus two tail test of significance 5% versus 1% alpha levels

35. -1.64 or +1.64 How would the critical z change? One-tailedTwo-tailed α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 What if our observed z = 1.75? Reject the null Do not Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z One versus two tail test of significance 5% versus 1% alpha levels

36. -1.64 or +1.64 How would the critical z change? One-tailedTwo-tailed α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 What if our observed z = 2.45? Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z One versus two tail test of significance 5% versus 1% alpha levels

37. Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule Alpha level? ( α =.05 or.01)? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed z (or t) is bigger then critical z (or t) then reject null Step 5: Conclusion - tie findings back in to research problem One or two tailed test? Balance between Type I versus Type II error Critical statistic (e.g. z or t or F or r) value?

39. What if we were looking to see if our new management program provides different results in employee happiness than the old program. What is the independent variable? a. The employees’ happiness b. Whether the new program works better c. The type of management program (new vs old) d. Comparing the null and alternative hypothesis One or two tailed test? The type of management program (new vs old) Two tailed because there is no prediction regarding who which will work better

40. Marietta is a manager of a movie theater. She wanted to know whether there is a difference in concession sales for afternoon (matinee) movies vs. evening movies. She took a random sample of 25 purchases from the matinee movie (mean of $7.50) and 25 purchases from the evening show (mean of $10.50). She compared these two means. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA What type of analysis is this? Let’s try one This is an example of a a. between participant design b. within participant design c. mixed participant design Let’s try another one t-test Between

41. What if we were looking to see if our new management program provides different results in employee happiness than the old program. What is the dependent variable? a. The employees’ happiness b. Whether the new program works better c. The type of management program (new vs old) d. Comparing the null and alternative hypothesis happiness

42. a. None of the employees are happy b. The program does not affect employee happiness c. The new programs works better d. The old program works better What if we were looking to see if our new management program provides different results in employee happiness than the old program. What would null hypothesis be? Remember the null says “no difference between groups” (between levels of IV) No difference

43. Which of the following is a Type I error: a. We conclude that the program works better when it fact it doesn’t b. We conclude that the program works better when in fact it does c. We conclude that the program doesn’t work better when in fact it doesn’t d. We conclude that the program doesn’t work better when in fact it does False alarm

44. Which of the following would represent a one-tailed test? a. Please test to see whether men or women are taller b. With an alpha of.05 test whether advertising increases sales c. With an alpha of.01 test whether management strategies affect worker productivity d. Does a stock trader’s education affect the amount of money they make in a year? Increases

45. Which of the following represents a significant finding: a. p < 0.05 b. critical value exceeds the observed statistic c. the observed z statistic is nearly zero d. we reject the null hypothesis e. Both a and d Careful with “exceeds” p < 0.05 and “reject null” both mean “significant finding”

46. Let’s try one Marietta took a pregnancy test. The null hypothesis would be: a. Marietta is pregnant b. Marietta is not pregnant “nothing going on”

47. Let’s try one Marietta took a pregnancy test and it read that she was pregnant, when it fact she was not. This is an example of a a. Type I error b. Type II error c. Type III error d. Correct decision False alarm = Type I error

48. Let’s try one Kenley decided to reject the null, and then found out the null was false. This is an example of a a. Type I error b. Type II error c. Type III error d. Correct decision It is right to reject a false null

49. Let’s try one Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results? a. as the sample size got larger the variability would increase b. as the sample size got larger the variability would decrease c. as the sample size got larger the variability would stay the same As n goes up, variability goes down

50. As n ↑ According to the Central Limit Theorem, which is false? As n ↑ x will approach µ As n ↑ curve will approach normal shape As n ↑ curve variability gets larger a. b. c. d. As n goes up, variability goes down

51. Let’s try one Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. Which of the following is true? a. The IV is gender while the DV is time to finish a race b. The IV is time to finish a race while the DV is gender IV = gender DV = time

52. Let’s try one a. The null hypothesis is that there is no difference in race times between the genders b. The null hypothesis is that there is a difference between the genders Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. Which of the following is true? No difference

53. Let’s try one Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. A Type I Error would claim that: a. There is a difference when in fact there is b. There is a difference when in fact there isn’t one c. There is no difference when in fact there isn’t one d. There is no difference when in fact there is a difference Which would be a Type II error? Type I = False Alarm Type II = Miss

54. Let’s try one Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides.. He concluded p < 0.05 what does this mean? a. There is a significant difference between the means b. There is no significant difference between the means p < 0.05 and “reject null” both mean “significant finding”

55. Let’s try one Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. Which is true? a. This is a one-tailed test b. This is a two-tailed test There is no prediction regarding who will be faster, males or females

56. Let’s try one Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. Which of the following is true? a. This is a quasi, between participant design b. This is a quasi, within participant design c. This is a true, between participant design d. This is a true, within participant design quasi, between

57. Let’s try one Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. Which of the following is best describes this study? a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA “t for two” (two groups being compared)

58. -1.64 or +1.64 Critical z values One-tailedTwo-tailed α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 5% 2.5% 1%.5% Match each level of significance to each situation. Which situation would be associated with a critical z of 1.96? a. A b. B c. C d. D A B CD Hint: Possible values 1.64 1.96 2.33 2.58

59. -1.64 or +1.64 Critical z values One-tailedTwo-tailed α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 5% 2.5% 1%.5% Match each level of significance to each situation. Which situation would be associated with a critical z of 1.64? a. A b. B c. C d. D A B CD Hint: Possible values 1.64 1.96 2.33 2.58

60. -1.64 or +1.64 Critical z values One-tailedTwo-tailed α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 5% 2.5% 1%.5% Match each level of significance to each situation. Which situation would be associated with a critical z of 2.58? a. A b. B c. C d. D A B CD Hint: Possible values 1.64 1.96 2.33 2.58

61. An advertising firm wanted to know whether the size of an ad in the margin of a website affected sales. They compared 4 ad sizes (tiny, small, medium and large). They posted the ads and measured sales. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between advertising space and sales More than two groups being compared

62. Afra was interested in whether caffeine affects time to complete a cross- word puzzle, and whether this affected young adults and older adults similarly. This is an example of a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA. Let’s try one Two separate IVs 1. caffeine – two levels (yes caffeine vs no caffeine) 2. Age – two levels (young vs old)

63. Gabriella is a manager of a movie theater. She wanted to know whether there is a difference in concession sales between teenage couples and middle-aged couples. She also wanted to know whether time of day makes a difference (matinee versus evening shows). She gathered the data for a sample of 25 purchases from each pairing. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between movie times and amount of concession purchases. Let’s try one Two separate IVs 1. Time of day – two levels (afternoon vs evening) 2. Age – two levels (young vs old)

64. Victoria was also interested in the effect of vacation time on productivity of the workers in her department. In her department some workers took vacations and some did not. She measured the productivity of those workers who did not take vacations and the productivity of those workers who did (after they returned from their vacations). This is an example of a _____. a. quasi-experiment b. true experiment c. correlational study Let’s try one Quasi- experiment She did not randomly assign groups, she let the workers self-select who will go on vacation

65. Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and he looked to see who sold more cookies. The 3 incentives were: 1) Trip to Hawaii, 2) New Bike or 3) Nothing. This is an example of a ___. a. quasi-experiment b. true experiment c. correlational study Let’s try one True- experiment He randomly assigned girls to groups

66. Marietta is a manager of a movie theater. She wanted to know whether there is a difference in concession sales for afternoon (matinee) movies vs. evening movies. She took a random sample of 25 purchases from the matinee movie (mean of $7.50) and 25 purchases from the evening show (mean of $10.50). She compared these two means. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between movie times and amount of concession purchases. Let’s try one “t for two” (two groups being compared)

67. Marietta is a manager of a movie theater. She wanted to know whether there is a difference in concession sales for afternoon (matinee) movies and evening movies. She took a random sample of 25 purchases from the matinee movie (mean of $7.50) and 25 purchases from the evening show (mean of $10.50). Which of the following would be the appropriate graph for these data Relationship between movie times and amount of concession purchases. Let’s try one Matinee Evening Concession purchase a. Movie Time Concession b. Movie Times Concession purchase d. c. Concession purchase Movie Times “t for two” (two groups being compared)

68. Pharmaceutical firm tested whether fish-oil capsules taken daily decrease cholesterol. They measured cholesterol levels for 30 male subjects and then had them take the fish-oil daily for 2 months and tested their cholesterol levels again. Then they compared the mean cholesterol before and after taking the capsules. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between daily fish-oil capsules and cholesterol levels in men. Let’s try one This is an example of a a. between participant design b. within participant design c. mixed participant design Let’s try another one “t for two” (fish-oil vs no fish-oil are the two groups being compared) Within (same people measured twice)

69. Elaina was interested in the relationship between the grade point average and starting salary. She recorded for GPA. and starting salary for 100 students and looked to see if there was a relationship. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between GPA and starting salary Let’s try one Relationship between GPA and Starting salary GPA Starting Salary Correlation (both variables are quantitative)

70. An automotive firm tested whether driving styles can affect gas efficiency in their cars. They observed 100 drivers and found there were four general driving styles. They recruited a sample of 100 drivers all of whom drove with one of these 4 driving styles. Then they asked all 100 drivers to use the same model car for a month and recorded their gas mileage. Then they compared the mean mpg for each driving style. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between driving strategy and gas mileage (miles per gallon). ANOVA Four groups being compared

71. Afra was interested in which characteristics of displays around the cash register will affect impulse purchases of candy bars and drinks. She was interested in the type of display (big versus little) and the location of the display (eye level versus waist level). She varied the location and type of display on different registers and recorded the number of sales of items on the displays (candy and drinks). This is an example of a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA. Let’s try one Two separate IVs 1. Type of display – two levels (big vs little) 2. Location – two levels (eye vs waist level)