PLSC-724 - ANSWERS FOR PRACTICE TEST ONE The normal curve becomes flatter as σ2 increases, and becomes more `peaked` as σ2 decreases. 1. The statistic estimates the parameter. Type I Error = 100 *α%. Decreasing σ from .05 to .01 decreases P(Type I Error). 2. Cost and lack of material b) increase 3. The probability of committing a Type II Error. 4. 1) Increase n 2) Decrease your estimate of σ2. 5. b) increase 6. The probability of committing a Type II Error. 7. a) Increase n. 8. Your ability to detect the alternate hypothesis when it is true. 9. Increase n (the number of observations) 10. a) Select a problem. b) Define the objectives. c) Define the population. 11. a) Unit of material to which one unit a of treatment is applied. b) A pen; 20 c) exp. error t(r-1)=15 sampling error tr(s-1)=60 total 79 d) 16 12. The mean of a population of values. 13. The soil. 14. Answer different for everyone.15. 1. Preliminary 2. Demonstration 3. Critical 16. 1. Choice of experimental design. 2. Use of covariance. 3. Size and shape of experimental units. 17. 1. To obtain a valid estimate of experimental error. 2. To increase precision. 18. Cost 19. Among 20. Square 21. As r increases, the Ys decreases, inversely as the r . 22. The variation among observations on experimental units treated alike. 23. The variation among observations on samples within experimental units. 24. Rep 1 Rep 2 Rep 3 Trt 1 28 31 34 Trt 2 20 18 21 Experimental error will be the variation among observations within treatment 1 and treatment 2. 25. a) Provide an unbiased estimate of experimental error. b) Provide an unbiased estimate of treatment effects. 26. Samples do not affect randomization. 27. a) Y... b) Yi.. 28. 1.4 29. b, c, d30. Null hypothesis: μa = μb + 10 Alternate hypothesis: μa > μb + 10 31. Fair to reject the null hypothesis. 32. The null hypothesis should be accepted. 33. t * 21YYss − standard error of the difference of two means = LSD 34. LSD does not take into consideration the number of treatments in the experiment. Tukey’s procedure does consider the number of treatments in the experiment. The basis of Tukey’s procedure is that as the number of treatments in an experiment increases, the likelihood that means will be similar decreases. Thus, the Significant Range Statistics values used in calculating the Tα-value increase as the number of treatments increases to off-set the decreasing likelihood of means being similar. 35. 4.0 36. 15 37. One-tail test. 38. a) When the experimental units are uniform. b) When the number of treatments is small. 39. Are the experimental units uniform? 40. Yijk = μ + τi +ε ij + λ ijk. μ = overall mean τ = treatment effect-deviation of treatment mean from the overall mean ε = random variation among observation on experimental units treated alike λ = random variation among samples within experimental units 41. ()'112iirrs + 42. a) b) 30 c) 15 d) 9 e) Variation among samples within experimental units 43. df for sample error = 20, the denominator = 8.44. . SOV df SS MS F Treatment 4 600 150 3.0 Exp. Error 15 750 50 Sampling Error 40 900 Total 59 2250 45. 126245165315343062222−++=STreatmentS 46. - 19 47. -7 48. 9 49. 4.71 50. 2Ys = 20 22`YYs− = 40 22`YYs− is used in calculating the LSD. 51. 20 52. Yijk = μ + τi + εj + δijk 53. Variation among observations on experimental units treated alike.54. Each treatment repeated the same number of times;