1. Jeopardy Statistics Edition

2. Terms Calculator Commands 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 A statement about the value of some population parameter that is assumed to be true.

8. Terms: $200 What is the null hypothesis or H 0 ? ?

9. Terms: $400 The probability of making a Type I error in a hypothesis test.

10. Terms: $400 What is the level of significance or  ? ?

11. Terms: $600 A range of plausible values for a population parameter that is determined from a single random sample.

12. Terms: $600 What is a confidence interval? ?

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. Calculator Commands: $200 To construct a confidence interval for the proportion of all XU students that will study for their final exam.

18. Calculator Commands: $200 What is “1-PropZInt…” ?

19. Calculator Commands: $400 To calculate a P-value for hypotheses involving a single population proportion.

20. Calculator Commands: $400 What is “normalcdf” ? ?

21. Calculator Commands: $600 To conduct a hypothesis test comparing two population means using the P-value approach.

22. Calculator Commands: $600 What is “2-SampTTest…” ?

23. Calculator Commands: $800 To construct a confidence interval for the difference in the proportion of females planning to study for finals and the proportion of men planning to study for finals.

24. Calculator Commands: $800 What is “2-PropZInt…” ?

25. Calculator Commands: $1000 To compute the P-value comparing the proportion of XU students that have various eye colors (blue, green, brown, hazel).

26. Calculator Commands: $1000 What is “  2 cdf” ? ?

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 A confidence interval has been constructed from a sample of size 100. If we are to construct another confidence interval with the ME ½ the margin of error of the first, this is the sample size needed.

46. Confidence Intervals: $1000 What is 400? ?

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 validity for a hypothesis test about a single population proportion.

52. Hyp. Tests: Proportions: $600 What is –(a) A properly obtained, random sample –(b) np ≥ 10 and n(1-p) ≥ 10 ?

53. Daily Double

54. Hyp. Tests: Proportions: $800 This is the test statistic obtained (give the calculation and the value) 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 do not know that results in having to use a Gosset t curve rather than the z-curve when performing tests about population means.

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 ?