2. BNAD 276: Statistical Inference in Management Spring 2016 Green sheets

4. Before our next exam (April 7 th ) OpenStax Chapters 1 – 12 Plous (2, 3, & 4) Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence Schedule of readings

5. Analysis of Variance (ANOVA) Constructing brief, complete summary statements Review for Exam 3 By the end of lecture today 4/5/16

6. Exam 3 – This Thursday, April 7 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 Nick and Jonathon When: Wednesday evening April 6 th - 6:30 – 8:30pm Where: Harvill 150 Cost: $5.00 Stats Review by Nick and Jonathon When: Wednesday evening April 6 th - 6:30 – 8:30pm Where: Harvill 150 Cost: $5.00

7. No homework Assignment Just study for Exam 3 Homework Assignment

8. small observed t score Remember, it never will be if the observed t is less than one Yes, p <.05, reject the null and it is a significant difference No, p is not <.05, do not reject the null and there is no significant difference

9. Decrease variability or decrease level of confidence It is easier to reject the null It gets narrower Easier; use a one-tail test when you have a unidirectional prediction Use a t-test when don’t know population standard deviation and only have sample standard deviation (Same is true for variance or variability)

10. Type of cartoon Two-tail True 48 2.011 Level of aggression Type of cartoon will not affect level of aggression Type of cartoon will affect level of aggression Type of cartoon will affect aggression when it fact it will not Type of cartoon will not affect aggression when it fact it will

11. Common and rare scores Mean approaches the true population mean Shape approaches normality Variability goes down Go down from.05 to.01 No, never reject null if the prediction in a one-tailed test is wrong

12. 9 14 71.7142 The mean test scores were 78 for the men and 79 for the women enrolled in Dr. Rubio’s class. A t-test was conducted and no significant difference was found, t(14) = -0.23; n.s. 7

13. 12 25100 The mean home prices were compared for these four neighborhoods. The average selling price was 65.5 million dollars in the Southpark neighborhood, 71 million dollars in the Northpark neighborhood, 77.25 million dollars for the Westpark neighborhood and 74.75 million dollars for the Eastpark neighborhood. An ANOVA was conducted and a significant main effect was found, F(3,12) = 4.00; p < 0.05. 3 43.49 Yes

14. 27 6.518 40 The mean number of cookies sold was 10 boxes for the girl scouts offered no incentive, 12 boxes for the girl scouts offered a new bike and 14 boxes for girl scouts offered a trip to Hawaii. An ANOVA conducted and a significant main effect was found, F(2, 27) = 6.14; p < 0.05 2 6.1 3.35 Yes

15. 58 42 42.1657.84 95% Mean ± (z)(standard deviation) 50 ± (1.96)(4) 50 ± (7.84)

16. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the random error variability (also known as the within variability)? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above 1. 2. 3. correct Review

17. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the between group variability? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above 1. 2. 3. correct Review

18. Let’s try one Which figure would depict the largest F ratio a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above Variability within groups Variability between groups F = 1. 2. 3. “F ratio” is referring to "observed F” correct Review

19. Let’s try one Winnie found an observed F ratio of.9, what should she conclude? a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given 1. 2. 3. correct Review

20. Let’s try one Winnie found an observed z of.74, what should she conclude? (Hint: notice that.74 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given small observed z score x x If your observed z is within one standard deviation of the mean, you will never reject the null correct Review

21. Let’s try one Winnie found an observed t of.04, what should she conclude? (Hint: notice that.04 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given small observed t score x correct Review

22. Let’s try one An ANOVA was conducted comparing different types of solar cells and there appears to be a significant difference in output of each (watts) F(4, 25) = 3.12; p < 0.05. In this study there were __ types of solar cells and __ total observations in the whole study? a. 4; 25 b. 5; 30 c. 4; 30 d. 5; 25 # groups - 1 # scores - # of groups # scores - 1 F(4, 25) = 3.12; p < 0.05 How many observations within each group? correct Review

23. Let’s try one An ANOVA was conducted comparing different types of solar cells and there appears to be significant difference in output of each (watts) F(4, 25) = 3.12; p < 0.05. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis p <.05 F(4, 25) = 3.12; p < 0.05 Observed F bigger than Critical F correct Review

24. Let’s try one An ANOVA was conducted comparing different types of solar cells. The analysis was completed using an alpha of 0.05. But Julia now wants to know if she can reject the null with an alpha of at 0.01. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis p <.05 F(4, 25) = 3.12; p < 0.05 Comparison of the Observed F and Critical F Is no longer are helpful because the critical F is no longer correct. We must use the p value p >.01 correct Review

25. Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Degrees of freedom between is _____; degrees of freedom within is ____ a. 16; 4 b. 4; 16 c. 12; 3 d. 3; 12. correct Review

26. Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Mean Square between is _____; Mean Square within is ____ a. 300, 300 b. 100, 100 c. 100, 25 d. 25, 100. correct

27. Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table. The F ratio is: a..25 b. 1 c. 4 d. 25. correct

28. An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table, alpha = 0.05. We should: a. reject the null hypothesis b. not reject the null hypothesis Let’s try one p <.05 Observed F bigger than Critical F correct

29. An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. The most expensive neighborhood was the ____ neighborhood a. Southpark b. Northpark c. Westpark d. Eastpark Let’s try one correct

30. An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table. The best summary statement is: a. F(3, 12) = 4.0; n.s. b. F(3, 12) = 4.0; p < 0.05 c. F(3, 12) = 3.49; n.s. d. F(3, 12) = 3.49; p < 0.05 correct

31. Let’s try one An ANOVA was conducted and there appears to be a significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 27) = ___; p < 0.05. Please fill in the blank a. 3.3541 b..00635 c. 6.1363 d. 27.00

32. Let’s try one An ANOVA was conducted comparing “best racquet” scores for different types of tennis racquets. The results were: F(4, 45) = 9.49; p < 0.05. What should we conclude? a. we rejected the null hypothesis b. we did not reject the null hypothesis F(4, 45) = 9.49; p < 0.01 correct

33. Let’s try one An ANOVA was conducted comparing “best racquet” scores for different types of tennis racquets. The results were: F(4, 45) = 9.49; p < 0.05. But Julia now wants to know if she can reject the null with an alpha of at 0.01. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis F(4, 45) = 9.49; p < 0.01 correct

34. Let’s try one An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). For each brand of ski we rated 10 skis. Degrees of freedom between is _____; degrees of freedom within is ____ a. 30; 3 b. 3; 30 c. 27; 2 d. 2; 27. correct

35. Let’s try one An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). For each brand of ski we rated 10 skis. Mean Square between is _____; Mean Square within is ____ a. 6.9, 1.5 b. 1.5, 6.9, c. 13.8, 41.5 d. 41.5, 13.8. correct

36. Let’s try one An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). For each brand of ski we rated 10 skis. The F ratio is: a..25 b. 1 c. 4.51 d. 25. correct

37. An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). Alpha = 0.05. Please complete this ANOVA table. We should: a. reject the null hypothesis b. not reject the null hypothesis Let’s try one p <.05 Observed F bigger than Critical F correct

38. An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). Alpha = 0.01. Please complete this ANOVA table. We should: a. reject the null hypothesis b. not reject the null hypothesis Let’s try one p NOT <.01 Observed F bigger than Critical F correct

39. An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). The best rated brand of skis was ____ a. 4FRNT b. K2 c. Rossignol Let’s try one correct

40. Let’s try one An ANOVA was conducted and there appears to be a significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 27) = ___; p < 0.05. Please fill in the blank a. 3.3541 b..00635 c. 6.1363 d. 27.00 correct

41. Let’s try one An ANOVA was conducted and we found the following results: F(3,12) = 3.73 ____. Which is the best summary a. The critical F is 3.89; we should reject the null b. The critical F is 3.89; we should not reject the null c. The critical F is 3.49; we should reject the null d. The critical F is 3.49; we should not reject the null correct

42. An ANOVA was conducted comparing which type of horse is the fastest (Arabians, Thoroughbreds, or Quarter Horses). We measured how long it took to finish the race. We measured 11 of each type of horse (33 altogether) Please complete this ANOVA table. Degrees of freedom between is _____; degrees of freedom within is ____ a. 30; 2 b. 2; 30 c. 80; 3 d. 3; 80 correct

43. An ANOVA was conducted comparing which type of horse is the fastest (Arabians, Thoroughbreds, or Quarter Horses). We measured how long it took to finish the race. We measured 11 of each type of horse (33 altogether) Mean Square Between is ____ while Mean Square Within is ______ a. 80; 2 b. 2; 80 c. 30; 40 d. 40; 30 correct

44. An ANOVA was conducted comparing which type of horse is the fastest (Arabians, Thoroughbreds, or Quarter Horses). We measured how long it took to finish the race. We measured 11 of each type of horse (33 altogether) Please complete this ANOVA table. The F ratio is a..75 b. 1.3 c. 1.5 d. 1.75 correct

45. The critical F ratio a. 2.84 b. 2.92 c. 3.23 d. 3.32 correct

46. The observed F is 1.3 and the critical F ratio is 3.32. What should we conclude? a. reject the null hypothesis b. do not reject the null hypothesis c. p < 0.5 d. both a and c are true correct

47. An ANOVA was conducted comparing which type of horse is the fastest (Arabians, Thoroughbreds, or Quarter Horses). We measured how long it took to finish the race. We measured 11 of each type of horse (33 altogether) Please complete this ANOVA table. The observed F is 2 and the critical F ratio is 3.32. F(2, 30) = ___; n.s. Please fill in the blank a. 3.32 b. 1.3 c. 30 d. 40 correct

48. an alpha of 0.01 Tasi is a small business owner who wanted to know whether her advertising campaign would make a difference in the average amount of money spent by her customers. She has two businesses, one in California and one in Florida. She completed an ad campaign in California, but had no advertising campaign in Florida. She then compared sales and completed a t-test using an alpha of 0.01. The results are presented in this table. Which of the following best describes the results of her experiment: a. There is a significant difference t(98) = 2.25; p <0.01 b. There is not a significant difference t(98) = 2.25; p <0.01 c. There is a significant difference t(98) = 2.25; n.s. d. There is not a significant difference t(98) = 2.25; n.s. Let’s try one correct

49. Let’s try one Theodora is researcher who compares how different companies address workers’ quality of life and general productivity. She created a questionnaire that measured these two constructs and gave the test to 140 men and 140 women. Please refer to this table to answer the following question: Which of the following best describe Theodora’s findings on worker productivity? a.A t-test was calculated and there is a significant difference in productivity between the two groups t(278) = 3.64; p < 0.05 b.A t-test was calculated and there is no significant difference in productivity between the two groups t(278) = 3.64; n.s. c.A t-test was calculated and there is a significant difference in productivity between the two groups t(280) = 3.64; p < 0.05 d.A t-test was calculated and there is no significant difference in productivity between the two groups t(280) = 3.64; n.s. correct

50. Let’s try one Refer again to Theodora’s findings presented on the table. Let’s assume for this question that Theodora set her alpha at 0.01, which of the following is true? a. Theodora found a significant difference between men and women’s quality of life, but not between men and women’s productivity. b.Theodora found a significant difference between men and women’s productivity, but not between men and women’s quality of life measures c. Theodora found a significant difference between men and women for both productivity and quality of life measures. d. Theodora found no significant difference between men and women for neither productivity nor quality of life measures. correct

51. .. 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? correct

52. Which of the following represents a significant finding: a. p < 0.05 b. the observed statistic (z score) is not bigger than critical value c. the observed z statistic is nearly zero d. do not reject the null hypothesis Careful with “exceeds” correct

53. A t-test was conducted to see whether “Bankers” or “Retailers” spend more time in front of their computer. Which best summarizes the results from this excel output: a. Bankers spent significantly more time in front of their computer screens than Retailers, t(3.5) = 8; p < 0.05 b. Bankers spent significantly more time in front of their computer screens than Retailers, t(8) = 3.5; p < 0.05 c. Retailers spent significantly more time in front of their computer screens than Bankers, t(3.5) = 8; p < 0.05 d. Retailers spent significantly more time in front of their computer screens than Bankers, t(8) = 3.5; p < 0.05 e. There was no difference between the groups correct

54. A t-test was conducted to see whether “Bankers” or “Retailers” spend more time in front of their computer. Which critical t would be the best to use a. 3.5 b. 1.859 c. 2.306 d..004 e..008 Let’s try one correct

55. A t-test was conducted to see whether “Bankers” or “Retailers” spend more time in front of their computer. How many bankers and retailers were measured a. 10 bankers were measured; 8 retailers were measured b. 10 bankers were measured; 10 retailers were measured c. 5 bankers were measured; 5 retailers were measured Let’s try one correct

56. 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. the means are the same, so the t-test would yield the same results. b. the means are the same, but the variability would increase so it would be harder to reject the null hypothesis. c. the means are the same, but the variability would decrease so it would be easier to reject the null hypothesis. correct

57. Let’s try one Albert compared the heights of a small sample of 10 women from the women’s gymnastics team to the mean for the whole team (population). This is an example of a one-sample t-test. He found an observed t(9) =.04, what should he do? a. Reject the null hypothesis b. Do not reject the null hypothesis c. There is not enough information correct

58. A table of t-test results How many of these t-tests reach significance with alpha of 0.05? a. 1b. 2c. 3d. 4 correct

59. 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 correct

60. According to the Central Limit Theorem, which is false? As n ↑ As n ↑ x will approach µ As n ↑ curve will approach normal shape As n ↑ curve variability gets bigger a. b. c. d. correct

61. Let’s try one Albert compared the race times of 20 male and female jockeys for 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 correct

62. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is true? 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 correct

63. Let’s try one Albert compared the race times of 20 male and female jockeys for 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? correct

64. Let’s try one Albert compared the race times of 20 male and female jockeys for 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 correct

65. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is true? a. This is a one-tailed test b. This is a two-tailed test correct

66. Let’s try one Albert compared the race times of 20 male and female jockeys for 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 a. This is a true, between participant design b. This is a true, within participant design correct

67. Let’s try one Albert compared the race times of 20 male and female jockeys for 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 correct

68. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is best describes his results? a. t(198) = 2.38; p < 0.05 b. t(198) = 2.38; ns c. t(198) = 1.97; p < 0.05 d. t(198) = 1.97; ns correct

69. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is best describes his results? a. t(198) = 2.38; p < 0.01 b. t(198) = 2.38; ns c. t(198) = 1.97; p < 0.01 d. t(198) = 1.97; ns correct

70. 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 correct

71. 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 correct

72. 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 correct

73. Ian was interested in the effect of incentives and age 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. He also measured their age. This is an example of a ___. a. quasi-experiment b. true experiment c. correlational study d. mixed design Let’s try one correct

74. 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 correct

75. 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 correct

76. 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. correct

77. 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 correct

78. -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

79. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the random error variability (also known as the within variability)? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above 1. 2. 3. correct