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Posted on Oct 05, 2024

A farmer would like to maximize his revenue through crop production. For this purpose, he seeks to determine which type of seed and type of

A farmer would like to maximize his revenue through crop production. For this purpose, he seeks to determine which type of seed and type of fertilizer produce the greatest crop yield. He is also interested in finding out if seed type and fertilizer type have any effect on the average crop yield. To this end, he randomly assigned different plots in a field to a combination of seed type (A, B, C or D) and fertilizer type (1, 2, 3 or 4), and measured the final crop yield in bushels per acre at harvest time. The resulting crop yields in bushels per acre for the different combinations are provided in file Assign3Data.xlsx.

a) [4 marks] Identify the experimental design and determine the number of treatments, experimental units and replicates.

b) [5 marks] Plot the residuals against the fitted values corresponding to the two-way ANOVA model for this analysis. What two key model assumptions can be examined with this plot and do they appear to be warranted?

c) [4 marks] Does the data provide enough evidence to indicate a significant interaction effect between type of seed and type of fertilizer? Conduct the appropriate hypothesis test at the 5% significance level; make sure you follow all the steps for hypothesis testing indicated in the Instructions section. Use software to generate the corresponding two- way ANOVA table, but show any other computations.

d) [2 marks] Create the corresponding interaction plot and explain if it shows interaction between type of seed and type of fertilizer impacting on crop yield; is this consistent with your results for part c) above?

e) [3 marks] Based on your answer to part c), does it make sense to test the effect of type of seed or the effect of type of fertilizer on the mean crop yield? If so, are these effects significant? Justify your answers.

f) [2 marks] Which combinations of seed type and fertilizer type (treatment means) have the lowest and highest average crop yield?

g) [4 marks] Calculate the Bonferroni margin of error for the confidence intervals based on all pairwise differences between the treatment means. Show your manual calculations and use an overall 95% confidence level. Why is it appropriate to use the Bonferroni method for comparing treatment means?

h) [2 marks] Using the calculated margin of error from part g) and the pairwise confidence interval approach, test the following statements:

For seed type A, does fertilizer type 1 vs. fertilizer type 2 make a significant difference on average crop yield?
For fertilizer type 4, does seed type A vs. seed type B make a significant difference on average crop yield?

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AutoSave OFF 6 A B Assign3Data - Saved to my Mac Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments Calibri (Body v 12 v AP A a Wras Text General SE X LG LIX V 1270 5 Paste B 1 - A = = = Insert Delete Format Ideas Merge & Center Conditional Format Cell Formatting as Table Styles Sort 2 Filter Find & Select V J28 . E E F H J K L M N P R S T T V W X Y 2 2 A 1 Seed type 2 2 A 3 A 4 4 A 5 A 7 A C Crop yield 5.19 4.98 4.78 4.89 4.69 4.96 S.CO 4.93 5.10 4.78 4.90 5.15 4.68 4.98 4.66 A A 4 A A A A A A A B Fertilizer type 1 1 1 1 1 1 1 1 1 1 1 1 Z 2 2 2 2 2 2 2 2 2 2 2 2 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | 29 30 31 32 A A 3 3 3 3 3 3 3 A A A A A A 4 A A A A A A A A 3 3 3 3 3 4 4 4,46 4.70 4.37 4.69 4.97 4.31 4.36 4.75 4.62 3.74 4.34 4.52 4.37 4,40 4.52 4.04 4.22 4.39 3.99 4.26 4.41 4,39 4.52 3.87 4.70 4 33 34 35 36 37 38 39 4 4 A 4 40 A A A 4 4 41 Question 1 Question 2 + + 100% AutoSave OFF OFF SUELO Assign3Data - Saved to my Mac Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments Calibri (body) v 12 v AP A a Wras Text General SE V LIX - 5 Paste B 1 A = = = Insert Delete Format Ideas Merge & Center Conditional Format Cell Formatting as Table Styles Sort 2 Filter Find & Select V J28 E E F H J K L M N P R S T T V W X Y 2 2 42 A B D B 1 1 1 1 4.59 4.58 448 4.55 B 1 B e 4.59 4.66 4.73 5.24 B D B A D 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 B A D 3 B 3 3 3 4.80 4.46 4.73 3.96 4.42 4.30 4.68 4.45 4.56 4.11 4.35 4.17 4.11 4.02 4.41 4.48 3.76 4.66 4,44 3.69 4.45 3.80 4.15 4.41 3.75 3.98 4,07 4.21 4.23 3.57 3 3 B e B D D 3 3 4 4 4 4 4 77 4 4 e B D 4 79 BO 81 82 4 1 1 Question 1 Question 2 + + 100% AutoSave OFF 6 A B Assign3Data - Saved to my Mac a Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments X Calibri (Body v 12 v AP A a Wras Text General LIX V + 28-0 5 Paste B 1 A = = = Merge & Center $ -% Insert Delete Format Ideas Conditional Format Cell Formatting as Table Styles Sort Filter Find & Select V J28 x A E E F H 1 J L M N O P R s T T V w X Y Z 3.77 3.90 4.49 4.00 83 84 es 86 87 88 89 90 91 4.66 C C C C C c C C C C C c C 1 1 1 1 1 1 1 1 1 1 1 2 2 2 92 93 4,64 4.31 4.43 4.20 3.94 4.70 3.88 95 C C 7 2 2 2 2 2 2 2 C C 3 3 C 3 3 3 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 C C C C C C 3 3 3.59 4.01 4.22 3.70 4.48 3.90 3.77 3.96 4.10 4.10 3.81 3.97 3.67 4.05 3.67 3.45 4.06 3.35 3.67 3.74 3.80 3.30 4.08 3.52 4.03 4.10 4.50 C C C C 4 4 4 4 4 4 4 4 4 C C C C C 4 4 1 1 D Question 1 Question 2 + + 100% AutoSave OFF 6 A B Assign3Data - Saved to my Mac Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments X Calibri (Body v 12 v AP A a Wras Text General SE LIX V 1270 5 Paste B 1 A = = = Insert Delete Format Ideas Merge & Center Conditional Format Cell Formatting as Table Styles Sort 2 Filter Find & Select V J28 A B E E F H J K L M N P R S T T V W X Y 2 2 124 1 1 D D D 1 1 1 1 D D D D 1 1 1 1 Z 4.47 4.42 4.56 4.69 4.42 4.17 4.31 4.59 4.07 4.13 4.25 4.23 4.57 4.33 4.17 4.47 125 126 127 128 179 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 2 D D D D D 2 Z 2 2 2 D D D 2 2 2 4.60 2 2 2 3 D D 4.02 3.99 4.18 3.82 3 146 3 3.94 D D D D D D D 3 3 3 3 3 4.41 4.14 4.15 4.06 3.90 3.56 3.91 4.05 3.91 D 4 4 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 D 4 4 D D 4 4 D D D D 4 4 4 4 4 3.61 3.72 3.69 3.79 3.45 162 163 164 Question 1 Question 2 + + 100% AutoSave OFF 6 A B Assign3Data - Saved to my Mac Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments Calibri (Body v 12 v AP A a Wras Text General SE X LG LIX V 1270 5 Paste B 1 - A = = = Insert Delete Format Ideas Merge & Center Conditional Format Cell Formatting as Table Styles Sort 2 Filter Find & Select V J28 . E E F H J K L M N P R S T T V W X Y 2 2 A 1 Seed type 2 2 A 3 A 4 4 A 5 A 7 A C Crop yield 5.19 4.98 4.78 4.89 4.69 4.96 S.CO 4.93 5.10 4.78 4.90 5.15 4.68 4.98 4.66 A A 4 A A A A A A A B Fertilizer type 1 1 1 1 1 1 1 1 1 1 1 1 Z 2 2 2 2 2 2 2 2 2 2 2 2 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | 29 30 31 32 A A 3 3 3 3 3 3 3 A A A A A A 4 A A A A A A A A 3 3 3 3 3 4 4 4,46 4.70 4.37 4.69 4.97 4.31 4.36 4.75 4.62 3.74 4.34 4.52 4.37 4,40 4.52 4.04 4.22 4.39 3.99 4.26 4.41 4,39 4.52 3.87 4.70 4 33 34 35 36 37 38 39 4 4 A 4 40 A A A 4 4 41 Question 1 Question 2 + + 100% AutoSave OFF OFF SUELO Assign3Data - Saved to my Mac Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments Calibri (body) v 12 v AP A a Wras Text General SE V LIX - 5 Paste B 1 A = = = Insert Delete Format Ideas Merge & Center Conditional Format Cell Formatting as Table Styles Sort 2 Filter Find & Select V J28 E E F H J K L M N P R S T T V W X Y 2 2 42 A B D B 1 1 1 1 4.59 4.58 448 4.55 B 1 B e 4.59 4.66 4.73 5.24 B D B A D 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 B A D 3 B 3 3 3 4.80 4.46 4.73 3.96 4.42 4.30 4.68 4.45 4.56 4.11 4.35 4.17 4.11 4.02 4.41 4.48 3.76 4.66 4,44 3.69 4.45 3.80 4.15 4.41 3.75 3.98 4,07 4.21 4.23 3.57 3 3 B e B D D 3 3 4 4 4 4 4 77 4 4 e B D 4 79 BO 81 82 4 1 1 Question 1 Question 2 + + 100% AutoSave OFF 6 A B Assign3Data - Saved to my Mac a Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments X Calibri (Body v 12 v AP A a Wras Text General LIX V + 28-0 5 Paste B 1 A = = = Merge & Center $ -% Insert Delete Format Ideas Conditional Format Cell Formatting as Table Styles Sort Filter Find & Select V J28 x A E E F H 1 J L M N O P R s T T V w X Y Z 3.77 3.90 4.49 4.00 83 84 es 86 87 88 89 90 91 4.66 C C C C C c C C C C C c C 1 1 1 1 1 1 1 1 1 1 1 2 2 2 92 93 4,64 4.31 4.43 4.20 3.94 4.70 3.88 95 C C 7 2 2 2 2 2 2 2 C C 3 3 C 3 3 3 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 C C C C C C 3 3 3.59 4.01 4.22 3.70 4.48 3.90 3.77 3.96 4.10 4.10 3.81 3.97 3.67 4.05 3.67 3.45 4.06 3.35 3.67 3.74 3.80 3.30 4.08 3.52 4.03 4.10 4.50 C C C C 4 4 4 4 4 4 4 4 4 C C C C C 4 4 1 1 D Question 1 Question 2 + + 100% AutoSave OFF 6 A B Assign3Data - Saved to my Mac Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments X Calibri (Body v 12 v AP A a Wras Text General SE LIX V 1270 5 Paste B 1 A = = = Insert Delete Format Ideas Merge & Center Conditional Format Cell Formatting as Table Styles Sort 2 Filter Find & Select V J28 A B E E F H J K L M N P R S T T V W X Y 2 2 124 1 1 D D D 1 1 1 1 D D D D 1 1 1 1 Z 4.47 4.42 4.56 4.69 4.42 4.17 4.31 4.59 4.07 4.13 4.25 4.23 4.57 4.33 4.17 4.47 125 126 127 128 179 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 2 D D D D D 2 Z 2 2 2 D D D 2 2 2 4.60 2 2 2 3 D D 4.02 3.99 4.18 3.82 3 146 3 3.94 D D D D D D D 3 3 3 3 3 4.41 4.14 4.15 4.06 3.90 3.56 3.91 4.05 3.91 D 4 4 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 D 4 4 D D 4 4 D D D D 4 4 4 4 4 3.61 3.72 3.69 3.79 3.45 162 163 164 Question 1 Question 2 + + 100%