A farmer has to decide between five different types of fertilizer (Fertilizer A, B, C, D and E) available on the market. He decides to test all five types in his orchard of orange trees to see which one works best. He decides to divide his orchard into five parts: part A, B, C, D and E. In part A he uses Fertilizer A, in part B Fertilizer B, etc. After the harvest he randomly chooses 15 trees from each part of the orchard. For each, he determines the total weight (in kg) of all the oranges on the tree and writes it down. Now he wants to test whether the type of fertilizer has an effect on the average weight of oranges in one orange tree. Use the below output to answer the questions that follow. One-way Analysis of Variance Output Y: Weight Factor: Fertilizer Number of observations: 75 ANOVA Table Degrees of Sum of Mean Source Freedom Squares Squares F-Value Prob > F Among Groups 4 649.5264 162.3816 (a) 0.0967 Within Groups 70 (b) 79.1842 Total 74 (c) Results of Bartlett's Chi-square test Bartlett's Degrees of Test Statistic Freedom p-value 2.897854 4 0.6151 Matrix of Tukey's Groupwise Comparisons Tests Group A B C D E A - 0.9796 0.1775 0.0923 0.9765 B - 0.2265 1.0000 1.0000 C - 0.2175 0.2357 D - 1.0000 E - 1) Bereken die ontbrekende waardes a, b en c in die ANOVA-tabel (Rond jou antwoord af tot 2 desimale) / Calculate the missing values a, b and c in the ANOVA-table (Round your answer to 2 desimals) a = Blank 1. Fill in the blank, read surrounding text. b = Blank 2. Fill in the blank, read surrounding text. c = Blank 3. Fill in the blank, read surrounding text. 2) Daar word getoets of daar 'n statisties betekenisvolle verskil is in die gemiddelde massas van lemoene uit die verskillende dele. Gee die p-waarde (presies soos in die uitvoer gegee) vir hierdie toets en stel of die nulhipotese verwerp word teen 'n 10% bekenispeil (Ja/Nee) / Whether there is a statistically significant difference in the mean weights of oranges from the different parts is tested. Give the p-value (exactly as given in the output) for this test and state whether the nulhypothesis is rejected at a 10% significance level (Yes/No). p-waarde/p-value: Blank 4. Fill in the blank, read surrounding text. Nulhipotese verwerp/Null hypothesis rejected: Blank 5. Fill in the blank, read surrounding text. 3) Daar word getoets of die variansies van die verskillende groepe homogeen is. Stel die p-waarde vir hierdie toets (presies soos in die uitvoer gegee). / It is tested whether the variances of the different groups are homogenous. State the p-value for this test (exactly as given in the output). p-waarde/p-value: Blank 6. Fill in the blank, read surrounding text.
A farmer has to decide between five different types of fertilizer (Fertilizer A, B, C, D and E) available on the market. He decides to test all five types in his orchard of orange trees to see which one works best. He decides to divide his orchard into five parts: part A, B, C, D and E. In part A he uses Fertilizer A, in part B Fertilizer B, etc. After the harvest he randomly chooses 15 trees from each part of the orchard. For each, he determines the total weight (in kg) of all the oranges on the tree and writes it down. Now he wants to test whether the type of fertilizer has an effect on the average weight of oranges in one orange tree. Use the below output to answer the questions that follow.
One-way Analysis of Variance Output
Y: Weight
Factor: Fertilizer
Number of observations: 75
ANOVA Table
Degrees of Sum of Mean
Source Freedom Squares Squares F-Value Prob > F
Among Groups 4 649.5264 162.3816 (a) 0.0967
Within Groups 70 (b) 79.1842
Total 74 (c)
Results of Bartlett's Chi-square test
Bartlett's Degrees of
Test Statistic Freedom p-value
2.897854 4 0.6151
Matrix of Tukey's Groupwise Comparisons Tests
Group A B C D E
A - 0.9796 0.1775 0.0923 0.9765
B - 0.2265 1.0000 1.0000
C - 0.2175 0.2357
D - 1.0000
E -
1) Bereken die ontbrekende waardes a, b en c in die ANOVA-tabel (Rond jou antwoord af tot 2 desimale) / Calculate the missing values a, b and c in the ANOVA-table (Round your answer to 2 desimals)
a = Blank 1. Fill in the blank, read surrounding text.
b = Blank 2. Fill in the blank, read surrounding text.
c = Blank 3. Fill in the blank, read surrounding text.
2) Daar word getoets of daar 'n statisties betekenisvolle verskil is in die gemiddelde massas van lemoene uit die verskillende dele. Gee die p-waarde (presies soos in die uitvoer gegee) vir hierdie toets en stel of die nulhipotese verwerp word teen 'n 10% bekenispeil (Ja/Nee) / Whether there is a statistically significant difference in the mean weights of oranges from the different parts is tested. Give the p-value (exactly as given in the output) for this test and state whether the nulhypothesis is rejected at a 10% significance level (Yes/No).
p-waarde/p-value: Blank 4. Fill in the blank, read surrounding text.
Nulhipotese verwerp/Null hypothesis rejected: Blank 5. Fill in the blank, read surrounding text.
3) Daar word getoets of die variansies van die verskillende groepe homogeen is. Stel die p-waarde vir hierdie toets (presies soos in die uitvoer gegee). / It is tested whether the variances of the different groups are homogenous. State the p-value for this test (exactly as given in the output).
p-waarde/p-value: Blank 6. Fill in the blank, read surrounding text.
4) Die gemiddeld van groep A verskil statisties betekenisvol van die gemiddeld van ten minste een ander groep, teen 'n 10% betekenispeil. Identifiseer hierdie groep(e) deur gebruik te maak van Tukey se groepsgewyse vergelykingstoets (HSD) (Tik slegs die letter(s) van hierdie groep(e) in die gegewe spasie) / The mean of group A differs statistically significantly from the mean of at least one other group, at a 10% significance level. Identify this group(s) by making use of Tukey's groupwise comparisons test (HSD) (Type only the letter(s) of these group(s) in the given space)
Antwoord/Answer: Blank 7. Fill in the blank, read surrounding text.
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