PLSC 724 - PRACTICE TEST ONE
1. Discuss briefly the relationship between the shape of the normal curve and the variance. Go To Answer 1
2. What is the relationship between a statistic and a parameter? Go To Answer 2
3. How is the alpha level related to the probability of a type 1 error? Go To Answer 3
4. The most common levels of significance used in statistical tests are the 5% and 1% levels.
Why are levels such as 0.1% or 0.01% not used? Go To Answer 4
5. Changing alpha from .05 to .01 causes beta to a) remain the same, b) increase, or c) decrease (choose the correct answer). Go To Answer 5
6. From the standpoint of types of error, what is beta? Go To Answer 6
7. List two ways in which beta can be reduced? Go To Answer 7
8. What is meant by the `power of the test` (in addition to being equal to 1 - beta)? Go To Answer 8
9. How can the power of the test be increased, while keeping alpha constant? Go To Answer 9
10. List two of the first three considerations to be made in planning an experiment. Go To Answer 10
11. Assume you are going to test five different feed rations on fattening steers. You put four steers in each of twenty pens. Four repetitions of each ration are assigned to the twenty pens at random. a) define an experimental unit; b) what, specifically, is an experimental unit in the above illustration? how many experimental units are there? c) what are the degrees of freedom for the sources of variation other than treatments? d) what is the numerical value for the denominator when calculating the standard error of a difference between two means. Go To Answer 11
12. A pharmaceutical company manufactures a pill that is said to contain 50 milligrams of a certain compound, together with some non-medical carrier to make it taste good. From a statistical standpoint, what does the number 50 represent? Go To Answer 12
13. Assume you have seven tractors and you want to measure differences in gas consumption while pulling a plow through soil for a specified distance. What are the experimental units? Go To Answer 13
14. Choose a subject matter area with which you are familiar and illustrate what an experimental unit is. Go Answer 14
15. Experiments can be placed into three categories (or types), name them. Go To Answer 15
16. List one means of `error control`. Go To Answer 16
17. What are two functions of replication? Go To Answer 17
18. What is the main reason most people do not use more replicates than they do? Go To Answer 18
19. In replicated experiments, we attempt to maximize the available variation (among, within) the replicates (choose one). Go To Answer 19
20. In field experiments, what is considered to be the best shape for the replicates? Go To Answer 20
21. What effect does the number of replicates have on the standard error of a mean? Go To Answer 21
22. Define experimental error. Go To Answer 22
23. Define sampling error. Go To Answer 23
24. Let t = 2 and r = 3 in a CRD. Illustrate precisely what contributes to experimental error. Go To Answer 24
25. What is the function of randomization? Go To Answer 25
26. Show and tell how to randomize a CRD where t = 4 and r = 3. If you planned to take two samples per experimental units, how would this affect the randomization procedure? Go To Answer 26
27. Assume you have a crd with sampling. Show, using the `dot` notation, symbols for a) the grand total, and b) a treatment total. Go To Answer 27
28. Using the following five numbers: 2, 5, 7, 7, 9, compute the variance of a mean. Go To Answer 28
.
29. Assume you are comparing two treatments with a paired comparison test. Which of the following sets of hypotheses are valid? There may be more than one answer. Go To Answer 29
a) null hypothesis: mu 1 = mu 2 + 10
alternate hypothesis: mu 1 does not equal mu 2
b) null hypothesis: mu 1 = or > mu 2
alternate hypothesis: mu 1 < mu 2
c) null hypothesis: mu 1 = mu 2
alternate hypothesis: mu 1 does not equal mu 2
d) null hypothesis: mu 1 = mu 2
alternate hypothesis: mu 1 minus mu 2 does not equal 0
30. It is hypothesized that treatment A will `yield` 10 units more than treatment B. If you are to test this hypothesis against the alternative that trt. A exceeds trt. B by more than 10 units, what should you have for the null and alternate hypothesis? Go To Answer 30
31. Given that mean 1 =16 and mean 2 = 22, and the LSD =7.3, should you accept or reject the null hypothesis of no difference between means? Go To Answer 31
32. If mean 1 = 30 and mean 2 = 52, should the null hypothesis of mu1 + 15 = mu2 be accepted or rejected if tabular `t`= 2.06 and the standard error of a difference between two means = 4? Go To Answer 32
33. What is the formula for the least significant difference. Go To Answer 33
34. What is the basic difference between the LSD and Duncan`s multiple range test? Go To Answer 34
35. Given the following data, calculate the standard error of a difference between treat means.
| SOV | df | SS |
| Treatments | 4 | 2304 |
| Experimental Error | 15 | 960 |
| Sampling Error | 20 | 320 |
36. If you were to calculate the LSD from data in problem 35, how many degrees of freedom would the tabular `t` have? Go To Answer 36
37. Assume you are using the F-test to compare treatment mean square with error mean square. Is this a one or two tailed F-test? Go To Answer 37
38. Under what two conditions is the CRD most appropriate? Go To Answer 38
39. Assume you have six weed control chemicals to evaluate on one variety of wheat under field conditions at Fargo. What would be the most important point to consider relative to possible uses of the CRD? Go To Answer 39
40. Write the linear model for an individual observation and define each term, for a CRD with sampling. Go To Answer 40
41. In a CRD, what is the formula for the standard error of a difference between two treatment means when ri does not equal rj. Go To Answer 41
42. Given a CRD with 5 treatment, 3 repetitions of each treatment and 3 samples within each experimental unit,
a) How many degrees of freedom are there for experimental error?
b) How many degrees of freedom are there for sampling error
c) How many experimental units are there?
d) What is the numerical value of the denominator when calculating the variance of the difference between two means?
e) What, precisely, contributes to `sampling error sum of squares`?`
f) What is the `expected mean square` for treatments if the null
hypothesis is false? Go To Answer 42
43. Assume you have a CRD with 5 treatments. Each treatment is repeated 4 times and there are two samples per experimental unit. How many degrees of freedom are there for sampling error? When you compute the standard error of a difference between two means, what is the numerical value for the denominator? Go To Answer 43
44. Complete the following anova table, given that t = 5, r = 4, and s = 3.
| SOV | df | SS | MS | F |
| Treatment | . | 600 | 150 | . |
| Experimental Error | . | 750 | . | . |
| Sampling Error | . | 900 | . | . |
45. The data in the following table represents a CRD. Show how you would compute treatment sums of squares.
| Treatment 1 | Treatment 2 | Treatment 3 |
| 80 | 51 | 29 |
| 69 | 59 | 37 |
| 74 | 43 | 26 |
| 83 | . | 33 |
| . | . | 40 |
| 306 | 153 | 165 |
y.. = 624 Go To Answer 45
46. Compute an estimate of Tau3 from question 45. Go To Answer 46
47. Compute an estimate of Epsilon 33 from question 45. Go To Answer 47
48. How many degrees of freedom are there for experimental error in question 45. Go To Answer 48
49. Given the error sum of square in question 45 is 375, compute the standard error appropriate for use in computing an LSD to compare treatments 2 and 3. Go To Answer 49
50. From the following analysis of variance table, compute the variance of the mean and the variance of the difference between 2 means. Which one is used in computing the LSD. Go To Answer 50
| SOV | df | SS |
| Treatments | 4 | 2800 |
| Exprimental Error | 15 | 3600 |
| Sampling Error | 40 | 4800 |
51. How many experimental units are there in problem 50? Go To Answer 51
52. Write the linear additive model appropriate for question 50. Go To Answer 52
53. Tell what gives rise to the exp err sum of squares in question 50. Go To Answer 53
54. Show symbolically how to compute treatment sums of squares when each treatment is repeated the same number of times and when treatments are repeated unequally. Go To Answer 54
55. Given the treatment totals shown below, fill in the squares so that exp. error ss equals zero.
| t1 | t2 | t3 | t4 | t5 |
| . | . | . | . | . |
| . | . | . | . | . |
| . | . | . | . | . |
| . | . | . | . | . |
| 36 | 18 | 23 | 34 | 42 |
56. Using information from question 56, calculate an estimate of Tau3. Go To Answer 56
57. Given that estimates of tau 1 thru tau 4 are 12, -6, 5, and -4, respectively, what is the estimate for Tau5? Go To Answer 57
58. Given that y bar.. = 22, Tau2 = 8, and Epsilon23 = -3, what is the numerical value of Y23? Go To Answer 58
59. Discuss briefly the relationship between the shape of the normal curve and the variance. Go To Answer 59
60. Given that variance 1 = 12 and variance 2 = 16, which population would have the flattest normal distribution? Which would have the greatest range. Go To Answer 60
61. What is the relationship between a statistic and a parameter? Go To Answer 61
62. List three measures of central tendency and define or illustrate each. Go To Answer 62
63. Which measure of central tendency provides a minimum sum of squares? Go To Answer 63
64. What is the best measure of dispersion? Go To Answer 64
65. Explain why the significant studentized range (SSR) value used in calculating the least square range (LSR) value for Duncan's new multiple range test increases as p (the number of treatments) increases. Go To Answer 65
66. An experiment was conducted using a CRD and the experimental error SS was 1.75. Given the following data and assuming the F-test on treatments was significant, indicate which treatment means are significantly different at the 95% level of confidence using lower case letters.
| Treatment | n | Mean |
| A | 5 | 2.3 |
| B | 7 | 2.7 |
| C | 5 | 2.9 |
67. Given the following data
| SOV | df | SS | MS |
| Treatment | 5 | 232.1 | 46.402 |
| Experimental Error | 12 | 15.2 | 1.267 |
| Sampling Error | 54 | 30.5 | 0.565 |
| Total | 71 | 277.8 |
a. How many experimental units are there in this experiment?
b. Determine if there are significant differences between treatments at the 95% and 99%
level of confidence using the appropriate F-test.
c. Calculate the CV for this experiment assuming Y...=434. Go To Answer 67
68. How is the precision of an experiment measured? Go To Answer 68
69. How can the precision of an experiment be increased? Go To Answer 69
70. Explain how the choice of experimental error can affect experimental error. Go To Answer 70
71. Why is the LSD value we calculate referred to as Fisher's-protected LSD? Go To Answer 71
72. What is the purpose of replication? Go To Answer 72
PlSc-724 - ANSWERS FOR PRACTICE TEST ONE
Answer 1. The normal curve becomes flatter as sigma square increases, and becomes more `peaked` as sigma square decreases.
Answer 2. The statistic estimates the parameter.
Answer 3. Type I Error = 100 alpha %. Decreasing alpha from .05 to .01 decreases P(Type I Error).
Answer 4. Cost and lack of material
Answer 5. b) increase
Answer 6. The probability of committing a Type II Error.
Answer 7. a) Increase n
b) Decrease your estimate of sigma square.
Answer 8. Your ability to detect the alternate hypothesis when it is true.
Answer 9. Increase n (the number of observations).
Answer 10. a) Select a problem.
b) Define the objectives.
Answer 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
Answer 12. The mean of a population of values.
Answer 13. The soil.
Answer 14. Answer different for everyone.
Answer 15. a) Preliminary
b) Demonstration
Answer 16. a) Choice of experimental design.
b) Use of covariance.
c) Size and shape of experimental units.
Answer 17. a) To obtain a valid estimate of experimental error.
Answer 18. Cost
Answer 19. Among
Answer 20. Square
Answer 21. As r increases, the standard error of a mean decreases inversely as the square root of r.
Answer 22. The variation among observations on experimental units treated alike.
Answer 23. The variation among observations on samples within exp. units.
Answer 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 trt 1 and trt 2.
Answer 25. a) Provide an unbiased estimate of experimental error. b)Provide an unbiased estimate of treatment effects.
Answer 26. Samples do not affect randomization.
Answer 27. a) Y...
Answer 28. 1.4
Answer 29. b, c, d
Answer 30. Null hypothesis: µa µb + 10
Alternate hypothesis: µa > µb + 10
Answer 31. Accept the null hypothesis
Answer 32. The null hypothesis should be accepted.
Answer 33. t x standard error of the difference of two means = LSD
Answer 34. LSD uses one number for comparisons between any two means. DMRT provides increasingly large values, which must be exceeded if two means are to be declared significantly different, as the number of means in the range increases. Thus, DMRT is slightly more conservative than the LSD.
Answer 35. 4.0
Answer 36. 15
Answer 37. One-tail test.
Answer 38. a) When the experimental units are uniform.
b) When the number of treatments is small.
Answer 39. Are the experimental units uniform?
Answer 40. Yijk = mu + taui + epsilonij + lambda ijk.
mu = overall mean
tau = treatment effect-deviation of treatment mean from the overall mean
epsilon = random variation among observation on experimental units treated alike
lambda = random variation among samples within experimental units
Answer 41. The square root of the following value: s2 (1/ri + 1/rj)
Answer 42. a) 10
b) 30
c) 15
d) 9
e) variation among samples within experimental units
f) sigma2 + s sigma2 + rs sigma2 +rs sigma2 tau
Answer 43. df for sample error = 20; the denominator = 8
| SOV | df | SS | MS | F |
| Treatment | 4 | 600 | 150 | 3.0 |
| Exp. Error | 15 | 750 | 50 | |
| Samp. Error | 40 | 900 | ||
| Total | 59 | 2250 |
Answer 45. Trt SS =(3062/4) + (1532/3) + (1652/5) - (6242/12)
Answer 46. - 19
Answer 47. - 7
Answer 49. 4.71
Answer 50. Variance of the mean = 20
Variance of the difference between 2 means = 40
The variance of the difference between 2 means is used in calculating the lsd.
Answer 51. 20
Answer 52. Yijk = mu + taui + epsilonj + deltaijk
Answer 53. Variation among observations on exp. units treated alike.
Answer 54. Each treatment repeated the same number of times;
Summation (Yi.2/r) - ((Y..)2/(rxt))
Each treatment repeated unequal number of times
((Yi.2/ri.) - Y..2)/(summation ri.)
| T1 | T2 | T3 | T4 | T5 |
| 9 | 4.5 | 5.75 | 8.5 | 10.5 |
| 9 | 4.5 | 5.75 | 8.5 | 10.5 |
| 9 | 4.5 | 5.75 | 8.5 | 10.5 |
| 9 | 4.5 | 5.75 | 8.5 | 10.5 |
| 36 | 18 | 23 | 34 | 42 |
Answer 56. -1.9
Answer 57 . -7
Answer 58. 27
Answer 59. The normal curve becomes flatter as sigma2 increases, and becomes more `peaked` as sigma2 decreases.
Answer 60. Population 2, Population 2
Answer 61. Parameter characterized a population and statistics characterize parameters.
Answer 62. a) mean - arithmetic average
b) median - central value
c) mode - most frequently observed value
Answer 63. Mean
Answer 64. Variance
Answer 65. SSR values increase as p increases to account for the fact that the probability of means being the same decreases as p increases.
| Treatment | n | Mean |
| A | 5 | 2.3 a |
| B | 7 | 2.7 b |
| C | 5 | 2.9 b |
Answer 67. a) 18
b) The F-test on treatments was significant at the 95 and 99% levels of confidence.
Answer 68. Precision is measured with the formula: Information=1/(variance of the mean)
Answer 69. a) Decrease the variance.
Answer 70. Design should be chose to minimize natural variation between experimental units so that differences between treatments are due to "true" differences between treatments. Also, the design affects error df. This can affect your likelihood of detecting differences between treatments.
Answer 71. We do not calculate the LSD unless the F-test for treatments is significant.
Answer 72. a) Provide an estimate of the variance.
b) Increase precision of the experiment.
c) Increase scope of the experiment.
d) Control error variance by grouping similar experimental units together.