1. Jeopardy Statistics Edition

2. Terms General Probability Sampling Distributions Confidence Intervals Hypothesis Tests: Proportions Hypothesis Tests: Means $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200

3. Final Jeopardy

4. CATEGORY: Hypothesis Tests

5. Final Jeopardy A sample of 80 is collected in which there are 62 successes. This is the type of error we risk making when testing the hypotheses: H 0 : p = 0.70 H a : p ≠ 0.70

6. Final Jeopardy What is a Type II error since we would Fail to Reject H 0 ? Running 1-PropZTest z = 1.464 P-value = 0.1432

7. Terms: $200 The number of outcomes in event E divided by the total number of possible outcomes.

8. Terms: $200 What is P(E) or the probability of event E? ?

9. Terms: $400 Two events that cannot occur simultaneously.

10. Terms: $400 What are disjoint or mutually exclusive events? ?

11. Terms: $600 Whether or not one event occurs has no bearing on whether or not another event occurs. P(E|F) = P(E)

12. Terms: $600 What are independent events? ?

13. Terms: $800 The probability of getting a sample comparable to the one we have under the assumption that the null hypothesis is correct.

14. Terms: $800 What is the P-value of a hypothesis test? ?

15. Terms: $1000 The value of some probability variable corresponding to the sample data collected.

16. Terms: $1000 What is the test statistic for a hypothesis test? ?

17. General Probability: $200 There are 20 marbles in a bag, 5 each of colors red, white, blue, and green. Each color is numbered 1 through 5. One marble is selected. This is the probability that it is blue.

18. General Probability: $200 What is 5/20 = 0.25? ?

19. General Probability: $400 There are 20 marbles in a bag, 5 each of colors red, white, blue, and green. Each color is numbered 1 through 5. One is selected at random. This is the probability that it is red or has the number 2 or 5 on it.

20. General Probability: $400 What is 11/20 = 0.55? ?

21. General Probability: $600 There are 20 marbles in a bag, 5 each of colors red, white, blue, and green. Each color is numbered 1 through 5. Three are selected at random without replacement. This is the probability that at least one of the marbles is blue.

22. General Probability: $600 What is 1 – (15/20)*(14/19)*(13/18) = 0.6009? ?

23. General Probability: $800 A check of dorm rooms on a certain college campus revealed that 38% had refrigerators (R), 54% had TVs (T), and 21% had both. This is the value and meaning of P(T|R C ).

24. General Probability: $800 What is the probability that the room has a TV given that it does not have a refrigerator? 0.33/(0.33 + 0.29) = 0.5323? ?

25. General Probability: $1000 A recent Maryland highway safety study found that in 77% of all accidents, the driver was wearing a seatbelt (S). Of those wearing a seatbelt, 92% escaped serious injury (I) but only 63% of those not wearing a seatbelt escaped serious injury. One driver is randomly selected. This is the meaning and value of P(S C |I C )

26. General Probability: $1000 What is the probability that the driver was not wearing a seatbelt given that (s)he did not escape serious injury? ?

27. Sampling Distributions: $200 At a certain company, it is believed that 84% of the employees approve the new benefits package that is being considered. A random sample of 68 employees is selected. These are the center, shape, and spread of the distribution of the sample proportion that approve the benefits package.

28. Sampling Distributions: $200 What is a normal distribution with mean 0.84 and standard deviation 0.0445? ?

29. Sampling Distributions: $400 At a certain company, it is believed that 84% of the employees approve the new benefits package that is being considered. A random sample of 68 employees is selected. This is the probability that less than 80% of the sample approve of the new benefits package.

30. Sampling Distributions: $400 What is 0.1844? ?

31. Sampling Distributions: $600 At a certain company, the average salary is $54000 with a standard deviation of $7800. A sample of 36 employees is chosen at random from this company. These are the center, shape, and spread of the distribution of the sample mean for such samples.

32. Sampling Distributions: $600 What is a normal distribution with mean $54000 and standard deviation $1300? ?

33. Sampling Distributions: $800 At a certain company, the average salary is $54000 with a standard deviation of $7800. A sample of 36 employees is chosen at random from this company. This is the probability that the average salary of this sample is more than $58000.

34. Sampling Distributions: $800 What is 0.0010? ?

35. Sampling Distributions: $1000 At a certain company, the average salary is $54000 with a standard deviation of $7800. A sample of 36 employees is chosen at random from this company. These average salaries make up the highest 0.5% of all such average salaries.

36. Sampling Distributions: $1000 What is $57348.58 and above? ?

37. Confidence Intervals: $200 This is the 97.4% CI for a population mean constructed from a sample of size 15 with mean 174.6mg and standard deviation 28.3mg if we assume the population is normally distributed.

38. Confidence Intervals: $200 What is (156.41mg, 192.79mg)? Using Tinterval with “Stats” given ?

39. Confidence Intervals: $400 This is equal to half the width of a confidence interval.

40. Confidence Intervals: $400 What is the margin of error of the confidence interval? ?

41. Confidence Intervals: $600 This is the minimum sample size that should be used if we want to construct a 95% CI for a population proportion with a margin of error of no more than 4.5 percentage points.

42. Confidence Intervals: $600 What is 475 subjects? ?

43. Confidence Intervals: $800 This is the minimum sample size that should be obtained if we want to construct a 90% CI for a population mean with margin of error no more than 7.2 when previous studies support that s = 42.8.

44. Confidence Intervals: $800 What is 96 subjects? ?

45. Confidence Intervals: $1000 This is what happens to a CI if we keep the confidence level the same but we increase the sample size.

46. Confidence Intervals: $1000 What is the margin of error decreases resulting in a more narrow confidence interval? ?

47. Hyp. Tests: Proportions: $200 This is the P-value of a two-tailed test that has test statistic z = -2.45.

48. Hyp. Tests: Proportions: $200 What is 0.0143? ?

49. Hyp. Tests: Proportions: $400 This is the P-value for a hypothesis test having: H 0 : p 1 = 0.2, p 2 = 0.4, p 3 = 0.3, p 4 = 0.1 Test statistic: X 2 = 10.42

50. Hyp. Tests: Proportions: $400 What is 0.0153? ?

51. Hyp. Tests: Proportions: $600 This is the “command” used in the calculator to, using the P-value approach, test the hypotheses : H 0 : p 1 = p 2 H a : p 1 < p 2

52. Hyp. Tests: Proportions: $600 What is2-PropZTest? ?

53. Daily Double

54. Hyp. Tests: Proportions: $800 This is the test statistic obtained from a sample of size 90 in which there were 62 ”successes” for the hypotheses: H 0 : p = 0.72 H a : p < 0.72

55. Hyp. Tests: Proportions: $800 What is z = -0.6573? ?

56. Hyp. Tests: Proportions: $1000 This is the 95% CI and conclusion reached for a sample of size 300 having 210 “successes” for the hypotheses: H 0 : p = 0.75 H a : p ≠ 0.75

57. Hyp. Tests: Proportions: $1000 What is (0.64814, 0.75186) and thus we Fail to Reject H 0 ? Using 1-PropZInt and noticing 0.75 is in the interval. ?

58. Hyp. Tests: Means: $200 This is what we must know in order to use the z statistic (rather than t) for a hypothesis test about a single population mean.

59. Hyp. Tests: Means: $200 What is σ, the population’s standard deviation? ?

60. Hyp. Tests: Means: $400 This is the validity needed when performing a ZTest.

61. Hyp. Tests: Means: $400 What is one of: (i) normal population (ii) large sample size (C.L.T.) (iii) a fairly linear normal plot ?

62. Hyp. Tests: Means: $600 This is the P-value for a sample of size 10 from a normal population that produced test statistic t = -1.34 for the hypotheses: H 0 : μ = 78 H a : μ ≠ 78

63. Hyp. Tests: Means: $600 What is 0.2131? ?

64. Hyp. Tests: Means: $800 This is the test statistic and P-value obtained from a sample of size 16 with mean 1472.4 hours and standard deviation 184.6 hours for the hypotheses: H 0 : μ = 1400 H a : μ > 1400

65. Hyp. Tests: Means: $800 What is t = 1.57 with P-value = 0.0686? ?

66. Hyp. Tests: Means: $1000 One employee at a certain company believes that women in the company are earning, on average, less than men. A random sample of men and women are selected from this company. For the 175 women, the average salary was $41250 with a standard deviation of $2100. For the 200 men in the sample the average salary was $42000 with a standard deviation of $2400. These are the test statistic, P-value, and conclusion for the hypotheses: H 0 : μ f = μ m H a : μ f < μ m

67. Hyp. Tests: Means: $1000 What is t = -3.227, P-value = 0.00068, and thus we Reject H 0 to conclude that on average, women do make less at this company than men? Using 2-SampTTest ?