Stress and Humor: Are They Related?

2. Practice A research was interested in the relation between stress and humor. Below are data from 8 subjects who completed tests of these two traits. Are these two variables related to each other? How much stress would a person probably experience if they had no sense of humor (i.e., score = 0)? How about if they had a high level of humor (i.e., score = 15)? Stress                Sense of Humor                        4                             2                      10                             8                      12                           11                        5                             3                        7                             8                        6                             7                        2                             3                      14                           13

3. Practice • r = .91 • Y = .77 + .98(Humor) • .77 = .77 + .98(0) • 15.47 = .77 + .98(15) • You don’t want to have a sense of humor

7. What is the probability of picking an ace?

8. Probability =

9. What is the probability of picking an ace? 4 / 52 = .077 or 7.7 chances in 100

10. Every card has the same probability of being picked

11. What is the probability of getting a 10, J, Q, or K?

12. (.077) + (.077) + (.077) + (.077) = .308 16 / 52 = .308

13. What is the probability of getting a 2 and then after replacing the card getting a 3 ?

14. (.077) * (.077) = .0059

15. What is the probability that the two cards you draw will be a black jack?

16. 10 Card = (.077) + (.077) + (.077) + (.077) = .308 Ace after one card is removed = 4/51 = .078 (.308)*(.078) = .024

17. Practice • What is the probability of rolling a “1” using a six sided dice? • What is the probability of rolling either a “1” or a “2” with a six sided dice? • What is the probability of rolling two “1’s” using two six sided dice?

18. Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? • What is the probability of rolling two “1’s” using two six sided dice?

19. Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? (.166) + (.166) = .332 • What is the probability of rolling two “1’s” using two six sided dice?

20. Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? (.166) + (.166) = .332 • What is the probability of rolling two “1’s” using two six sided dice? (.166)(.166) = .028

21. Next step • Is it possible to apply probabilities to a normal distribution?

22. Theoretical Normal Curve -3 -2 -1 1 2  3 

23. Theoretical Normal Curve -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

24. We can use the theoretical normal distribution to determine the probability of an event. For example, do you know the probability of getting a Z score of 0 or less? .50 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

25. We can use the theoretical normal distribution to determine the probability of an event. For example, you know the probability of getting a Z score of 0 or less. .50 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

26. With the theoretical normal distribution we know the probabilities associated with every z score! The probability of getting a score between a 0 and a 1 is .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

27. What is the probability of getting a score of 1 or higher? .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

28. These values are given in Table C on page 400 .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

29. To use this table look for the Z score in column AColumn B is the area between that score and the mean Column B .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

30. To use this table look for the Z score in column AColumn C is the area beyond the Z score Column C .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

31. The curve is symmetrical -- so the answer for a positive Z score is the same for a negative Z score Column B Column C .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

32. Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? • Beyond z = 2.25? • Between the mean and z = -1.45

33. Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? • Between the mean and z = -1.45

34. Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? .0122 • Between the mean and z = -1.45

35. Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? .0122 • Between the mean and z = -1.45 .4265

36. Practice • What proportion of this class would have received an A on the last test if I gave A’s to anyone with a z score of 1.25 or higher? • .1056

38. Note • This is using a hypothetical distribution • Due to chance, empirical distributions are not always identical to theoretical distributions • If you sampled an infinite number of times they would be equal! • The theoretical curve represents the “best estimate” of how the events would actually occur

39. Theoretical Distribution

40. Empirical Distribution based on 52 draws

41. Empirical Distribution based on 52 draws

42. Empirical Distribution based on 52 draws

43. Theoretical Normal Curve 

44. Empirical Distribution

45. Empirical Distribution

46. Empirical Distribution

47. PROGRAM http://www.mathsisfun.com/data/quincunx.html

48. Theoretical Normal Curve  Normality frequently occurs in many situations of psychology, and other sciences

50. Practice • #7.7 • #7.8 • #7.9