chi square and f distributions introduction to two way anova Questions
1 In a two-way ANOVA, factor A has a levels and factor B has b levels. The number of data values in each group is n. Find the degrees of freedom for factor A and factor B.
A ) (a - 1)(b - 1), ab(n - 1)
B ) a - 1, b - 1
C ) a + 1, b + 1
D ) a, b
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2 In a two-way ANOVA, factor A has a levels and factor B has b levels. The number of data values in each group is n. Find the degrees of freedom for factor A and factor B.
A ) (a - 1)(b - 1), ab(n - 1)
B ) a - 1, b - 1
C ) a + 1, b + 1
D ) a, b
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3 In a two-way ANOVA, factor A has a levels and factor B has b levels. The number of data values in each group is n. Find the degrees of freedom for factor A and factor B.
A ) (a - 1)(b - 1), ab(n - 1)
B ) a - 1, b - 1
C ) a + 1, b + 1
D ) a, b
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4 In a two-way ANOVA, factor A has a levels and factor B has b levels. The number of data values in each group is n. Find the degrees of freedom for factor A × B (Interaction) and for the Within (error) factor.
A ) a - 1, b - 1
B ) a + 1, b + 1
C ) a, b
D ) (a - 1)(b - 1), ab(n - 1)
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5 In a two-way ANOVA, factor A has a levels and factor B has b levels. The number of data values in each group is n. Find the degrees of freedom for factor A × B (Interaction) and for the Within (error) factor.
A ) a - 1, b - 1
B ) a + 1, b + 1
C ) a, b
D ) (a - 1)(b - 1), ab(n - 1)
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6 In a two-way ANOVA, factor A has a levels and factor B has b levels. The number of data values in each group is n. Find the degrees of freedom for factor A × B (Interaction) and for the Within (error) factor.
A ) a - 1, b - 1
B ) a + 1, b + 1
C ) a, b
D ) (a - 1)(b - 1), ab(n - 1)
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7 In a two-way ANOVA, variable A has three levels and variable B has two levels. The number of data values in each group is five. Find the degrees of freedom for factor A × B and for the within (error) factor.
A ) 2, 24
B ) 4, 3
C ) 2, 1
D ) 3, 2
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8 In a two-way ANOVA, variable A has three levels and variable B has two levels. The number of data values in each group is five. Find the degrees of freedom for factor A × B and for the within (error) factor.
A ) 2, 24
B ) 4, 3
C ) 2, 1
D ) 3, 2
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9 In a two-way ANOVA, variable A has three levels and variable B has two levels. The number of data values in each group is five. Find the degrees of freedom for factor A × B and for the within (error) factor.
A ) 2, 24
B ) 4, 3
C ) 2, 1
D ) 3, 2
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10 In a two-way ANOVA, factor A has six levels and factor B has five levels. The number of data values in each group is seven. Find the degrees of freedom for factor A and factor B.
A ) 7, 6
B ) 5, 4
C ) 6, 5
D ) 20, 180
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11 In a two-way ANOVA, factor A has six levels and factor B has five levels. The number of data values in each group is seven. Find the degrees of freedom for factor A and factor B.
A ) 7, 6
B ) 5, 4
C ) 6, 5
D ) 20, 180
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12 In a two-way ANOVA, factor A has six levels and factor B has five levels. The number of data values in each group is seven. Find the degrees of freedom for factor A and factor B.
A ) 7, 6
B ) 5, 4
C ) 6, 5
D ) 20, 180
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13 The means of each group of a two-way analysis of variance for two independent variables are plotted as shown in the graph. What does the graph represent about the interaction of the variables?
A ) Disordinal interaction
B ) Ordinal interaction
C ) No interaction
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14 The means of each group of a two-way analysis of variance for two independent variables are plotted as shown in the graph. What does the graph represent about the interaction of the variables?
A ) Disordinal interaction
B ) Ordinal interaction
C ) No interaction
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15 The means of each group of a two-way analysis of variance for two independent variables are plotted as shown in the graph. What does the graph represent about the interaction of the variables?
A ) Disordinal interaction
B ) Ordinal interaction
C ) No interaction
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16 The means of each group of a two-way analysis of variance for two independent variables are plotted and shown in the three graphs. Which of these represents a disordinal interaction? Consider the interaction to be significant.
A ) Both graph 1 and graph 2
B ) Graph 1
C ) Graph 3
D ) Graph 2
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17 The means of each group of a two-way analysis of variance for two independent variables are plotted and shown in the three graphs. Which of these represents a disordinal interaction? Consider the interaction to be significant.
A ) Both graph 1 and graph 2
B ) Graph 1
C ) Graph 3
D ) Graph 2
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18 The means of each group of a two-way analysis of variance for two independent variables are plotted and shown in the three graphs. Which of these represents a disordinal interaction? Consider the interaction to be significant.
A ) Both graph 1 and graph 2
B ) Graph 1
C ) Graph 3
D ) Graph 2
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19 The means of each group of a two-way analysis of variance for two independent variables are plotted and shown in the three graphs. Which of these represents an ordinal interaction? Consider the interaction to be significant.
A ) Graph 2
B ) Both graph 1 and graph 2
C ) Graph 3
D ) Graph 1
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20 The means of each group of a two-way analysis of variance for two independent variables are plotted and shown in the three graphs. Which of these represents an ordinal interaction? Consider the interaction to be significant.
A ) Graph 2
B ) Both graph 1 and graph 2
C ) Graph 3
D ) Graph 1
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21 The means of each group of a two-way analysis of variance for two independent variables are plotted and shown in the three graphs. Which of these represents an ordinal interaction? Consider the interaction to be significant.
A ) Graph 2
B ) Both graph 1 and graph 2
C ) Graph 3
D ) Graph 1
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22 Which of the following are the assumptions for two-way ANOVA? I. All samples are drawn from normally distributed populations. II. All populations have a common variance. III. The groups must be equal in sample size. IV. Within each group, the observations were sampled randomly and independently of each other.
A ) I and II
B ) I, II, III, and IV
C ) I, II, and III
D ) Only I
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23 Which of the following are the assumptions for two-way ANOVA? I. All samples are drawn from normally distributed populations. II. All populations have a common variance. III. The groups must be equal in sample size. IV. Within each group, the observations were sampled randomly and independently of each other.
A ) I and II
B ) I, II, III, and IV
C ) I, II, and III
D ) Only I
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24 Which of the following are the assumptions for two-way ANOVA? I. All samples are drawn from normally distributed populations. II. All populations have a common variance. III. The groups must be equal in sample size. IV. Within each group, the observations were sampled randomly and independently of each other.
A ) I and II
B ) I, II, III, and IV
C ) I, II, and III
D ) Only I
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25 30 people were randomly assigned to one of six experimental conditions. At the end of the lecture, a measure of comprehension was obtained. The data is shown here. At α = 0.05, find the test value FA × B and check the interaction of the variables using a two-way ANOVA. [ A : Presentation and B : Lecture ]
A ) 1.95, the type of lecture and the method of presentation does not affect the scores of students
B ) 8.74, the type of lecture and the method of presentation affect the scores of students
C ) 18.6, the type of lecture and the method of presentation affect the scores of students
D ) 3.4, the type of lecture and the method of presentation does not affect the scores of students
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26 30 people were randomly assigned to one of six experimental conditions. At the end of the lecture, a measure of comprehension was obtained. The data is shown here. At α = 0.05, find the test value FA × B and check the interaction of the variables using a two-way ANOVA. [ A : Presentation and B : Lecture ]
A ) 1.95, the type of lecture and the method of presentation does not affect the scores of students
B ) 8.74, the type of lecture and the method of presentation affect the scores of students
C ) 18.6, the type of lecture and the method of presentation affect the scores of students
D ) 3.4, the type of lecture and the method of presentation does not affect the scores of students
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27 30 people were randomly assigned to one of six experimental conditions. At the end of the lecture, a measure of comprehension was obtained. The data is shown here. At α = 0.05, find the test value FA × B and check the interaction of the variables using a two-way ANOVA. [ A : Presentation and B : Lecture ]
A ) 1.95, the type of lecture and the method of presentation does not affect the scores of students
B ) 8.74, the type of lecture and the method of presentation affect the scores of students
C ) 18.6, the type of lecture and the method of presentation affect the scores of students
D ) 3.4, the type of lecture and the method of presentation does not affect the scores of students
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28 16 individuals with high blood pressure(mmHg) were randomly subjected to one of four types of treatments. At the end of the treatment period, blood pressure was assessed: At α = 0.05, find FA , FB. Is there any difference in the mean blood pressure of individuals under (i) Drug therapy (ii) Diet modification ? Use a two-way ANOVA. [ A : Drug therapy and B : Diet modification ]
A ) 5.47, 27.92, (i) no, (ii) yes
B ) 27.92, 5.47, (i) yes, (ii) yes
C ) 5.47, 0.23, (i) no, (ii) no
D ) 27.92, 0.23, (i) yes, (ii) no
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29 16 individuals with high blood pressure(mmHg) were randomly subjected to one of four types of treatments. At the end of the treatment period, blood pressure was assessed: At α = 0.05, find FA , FB. Is there any difference in the mean blood pressure of individuals under (i) Drug therapy (ii) Diet modification ? Use a two-way ANOVA. [ A : Drug therapy and B : Diet modification ]
A ) 5.47, 27.92, (i) no, (ii) yes
B ) 27.92, 5.47, (i) yes, (ii) yes
C ) 5.47, 0.23, (i) no, (ii) no
D ) 27.92, 0.23, (i) yes, (ii) no
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30 16 individuals with high blood pressure(mmHg) were randomly subjected to one of four types of treatments. At the end of the treatment period, blood pressure was assessed: At α = 0.05, find FA , FB. Is there any difference in the mean blood pressure of individuals under (i) Drug therapy (ii) Diet modification ? Use a two-way ANOVA. [ A : Drug therapy and B : Diet modification ]
A ) 5.47, 27.92, (i) no, (ii) yes
B ) 27.92, 5.47, (i) yes, (ii) yes
C ) 5.47, 0.23, (i) no, (ii) no
D ) 27.92, 0.23, (i) yes, (ii) no
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31 We have a drug trial where two drugs (M, N) are each tested at two dosage levels (1X, 2X). The reaction time (in seconds) of three patients who were administered the drugs are tabulated as shown: At α = 0.05, find FA × B. Find whether there is any interaction effect between the kind of drug and the dosage level on the mean reacting time using a two-way ANOVA. [ A : Drug and B : Dosage ]
A ) 7.17, yes
B ) 5.32, yes
C ) 0.73, no
D ) 97.2, no
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32 We have a drug trial where two drugs (M, N) are each tested at two dosage levels (1X, 2X). The reaction time (in seconds) of three patients who were administered the drugs are tabulated as shown: At α = 0.05, find FA × B. Find whether there is any interaction effect between the kind of drug and the dosage level on the mean reacting time using a two-way ANOVA. [ A : Drug and B : Dosage ]
A ) 7.17, yes
B ) 5.32, yes
C ) 0.73, no
D ) 97.2, no
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33 We have a drug trial where two drugs (M, N) are each tested at two dosage levels (1X, 2X). The reaction time (in seconds) of three patients who were administered the drugs are tabulated as shown: At α = 0.05, find FA × B. Find whether there is any interaction effect between the kind of drug and the dosage level on the mean reacting time using a two-way ANOVA. [ A : Drug and B : Dosage ]
A ) 7.17, yes
B ) 5.32, yes
C ) 0.73, no
D ) 97.2, no
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34 In a medical school a new method of teaching in which professional actors played the roles of patients was introduced. The test scores of male and female students who were taught by either the conventional method or by a new form of training using role-play are shown in the table. Find FA , FB. Is there any difference in the mean test score under (i) Gender (ii) Teaching Method, using a two-way ANOVA at α = 0.05. [A : Gender and B : Teaching Method ]
A ) 57.45, 0.771, (i) no, (ii)yes
B ) 21.04, 57.45, (i) no, (ii) no
C ) 21.04, 0.771, (i) yes, (ii) no
D ) 21.04, 57.45, (i) yes, (ii) yes
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35 In a medical school a new method of teaching in which professional actors played the roles of patients was introduced. The test scores of male and female students who were taught by either the conventional method or by a new form of training using role-play are shown in the table. Find FA , FB. Is there any difference in the mean test score under (i) Gender (ii) Teaching Method, using a two-way ANOVA at α = 0.05. [A : Gender and B : Teaching Method ]
A ) 57.45, 0.771, (i) no, (ii)yes
B ) 21.04, 57.45, (i) no, (ii) no
C ) 21.04, 0.771, (i) yes, (ii) no
D ) 21.04, 57.45, (i) yes, (ii) yes
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36 In a medical school a new method of teaching in which professional actors played the roles of patients was introduced. The test scores of male and female students who were taught by either the conventional method or by a new form of training using role-play are shown in the table. Find FA , FB. Is there any difference in the mean test score under (i) Gender (ii) Teaching Method, using a two-way ANOVA at α = 0.05. [A : Gender and B : Teaching Method ]
A ) 57.45, 0.771, (i) no, (ii)yes
B ) 21.04, 57.45, (i) no, (ii) no
C ) 21.04, 0.771, (i) yes, (ii) no
D ) 21.04, 57.45, (i) yes, (ii) yes
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37 A bakery company supplies wrapped Italian bread to a large number of supermarkets in a metropolitan area. A study conducted on the effects of height and width of the display on sales. Twelve supermarkets, similar in sales volume and clientele, were used. Two stores were assigned at random to each of the treatments. Sales were recorded. Find the test values FA , FB and FA × B using a two-way ANOVA.[ A : Display height and B : Display width ]
A ) 5.14, 5.99, 5.14
B ) 1.16, 74.7, 1.16
C ) 5.14, 1.16, 5.99
D ) 74.7, 1.16, 1.16
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38 A bakery company supplies wrapped Italian bread to a large number of supermarkets in a metropolitan area. A study conducted on the effects of height and width of the display on sales. Twelve supermarkets, similar in sales volume and clientele, were used. Two stores were assigned at random to each of the treatments. Sales were recorded. Find the test values FA , FB and FA × B using a two-way ANOVA.[ A : Display height and B : Display width ]
A ) 5.14, 5.99, 5.14
B ) 1.16, 74.7, 1.16
C ) 5.14, 1.16, 5.99
D ) 74.7, 1.16, 1.16
View Solution
39 A bakery company supplies wrapped Italian bread to a large number of supermarkets in a metropolitan area. A study conducted on the effects of height and width of the display on sales. Twelve supermarkets, similar in sales volume and clientele, were used. Two stores were assigned at random to each of the treatments. Sales were recorded. Find the test values FA , FB and FA × B using a two-way ANOVA.[ A : Display height and B : Display width ]
A ) 5.14, 5.99, 5.14
B ) 1.16, 74.7, 1.16
C ) 5.14, 1.16, 5.99
D ) 74.7, 1.16, 1.16
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40 A web-designing company wants to learn about the effect of one-click checkouts. The target audiences of the web site were randomized into four groups, with 4 in each group. Each group was shown a page with either high or low graphics layout, and with one, or two click out options. After using the page, customers rated the convenience of the design on a 0-50 scale. At α = 0.05, find FA × B and analyze the interaction effect using a two-way ANOVA. [ A : Page layout and B : Mouse click ]
A ) 44.1, the combination of page layout and mouse click does not affect the scores
B ) 44.1, the combination of page layout and mouse click does affect the scores
C ) 0.1, the combination of page layout and mouse click does not affect the scores
D ) 4.75, the combination of page layout and mouse click does affect the scores
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41 A web-designing company wants to learn about the effect of one-click checkouts. The target audiences of the web site were randomized into four groups, with 4 in each group. Each group was shown a page with either high or low graphics layout, and with one, or two click out options. After using the page, customers rated the convenience of the design on a 0-50 scale. At α = 0.05, find FA × B and analyze the interaction effect using a two-way ANOVA. [ A : Page layout and B : Mouse click ]
A ) 44.1, the combination of page layout and mouse click does not affect the scores
B ) 44.1, the combination of page layout and mouse click does affect the scores
C ) 0.1, the combination of page layout and mouse click does not affect the scores
D ) 4.75, the combination of page layout and mouse click does affect the scores
View Solution
42 A web-designing company wants to learn about the effect of one-click checkouts. The target audiences of the web site were randomized into four groups, with 4 in each group. Each group was shown a page with either high or low graphics layout, and with one, or two click out options. After using the page, customers rated the convenience of the design on a 0-50 scale. At α = 0.05, find FA × B and analyze the interaction effect using a two-way ANOVA. [ A : Page layout and B : Mouse click ]
A ) 44.1, the combination of page layout and mouse click does not affect the scores
B ) 44.1, the combination of page layout and mouse click does affect the scores
C ) 0.1, the combination of page layout and mouse click does not affect the scores
D ) 4.75, the combination of page layout and mouse click does affect the scores
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43 The Principal was interested in studying the effect of different room temperatures (60 and 100 degrees) on test taking which had two levels of test difficulty (hard and easy). The scores of students(out of 100) taking the test are as follows. At α = 0.05, find FA , FB. Is there any difference in the mean test score under (i) test difficulty (ii) room temperature, using a two-way ANOVA.[A : test difficulty and B : room temperature ]
A ) 32.3, 0.66, (i) yes, (ii) yes
B ) 87.8, 32.3, (i) yes, (ii) yes
C ) 32.3, 87.8, (i) no, (ii) no
D ) 87.8, 0.66, (i) no, (ii) no
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44 The Principal was interested in studying the effect of different room temperatures (60 and 100 degrees) on test taking which had two levels of test difficulty (hard and easy). The scores of students(out of 100) taking the test are as follows. At α = 0.05, find FA , FB. Is there any difference in the mean test score under (i) test difficulty (ii) room temperature, using a two-way ANOVA.[A : test difficulty and B : room temperature ]
A ) 32.3, 0.66, (i) yes, (ii) yes
B ) 87.8, 32.3, (i) yes, (ii) yes
C ) 32.3, 87.8, (i) no, (ii) no
D ) 87.8, 0.66, (i) no, (ii) no
View Solution
45 The Principal was interested in studying the effect of different room temperatures (60 and 100 degrees) on test taking which had two levels of test difficulty (hard and easy). The scores of students(out of 100) taking the test are as follows. At α = 0.05, find FA , FB. Is there any difference in the mean test score under (i) test difficulty (ii) room temperature, using a two-way ANOVA.[A : test difficulty and B : room temperature ]
A ) 32.3, 0.66, (i) yes, (ii) yes
B ) 87.8, 32.3, (i) yes, (ii) yes
C ) 32.3, 87.8, (i) no, (ii) no
D ) 87.8, 0.66, (i) no, (ii) no
View Solution
46 An automobile company has two factories, and each factory makes the same three models of car. At α = 0.05, find the test values FA , FB. Is there any difference in the mean mileage depending on the (i) factory (ii) type of model using a two-way ANOVA.[ A : Factory and B : Type of model ]
A ) 13.09, 32.3, (i) no, (ii) yes
B ) 4.7, 3.9, (i) yes, (ii) yes
C ) 13.09, 32.3, (i) yes, (ii) yes
D ) 4.7, 3.9, (i) no, (ii) no
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47 An automobile company has two factories, and each factory makes the same three models of car. At α = 0.05, find the test values FA , FB. Is there any difference in the mean mileage depending on the (i) factory (ii) type of model using a two-way ANOVA.[ A : Factory and B : Type of model ]
A ) 13.09, 32.3, (i) no, (ii) yes
B ) 4.7, 3.9, (i) yes, (ii) yes
C ) 13.09, 32.3, (i) yes, (ii) yes
D ) 4.7, 3.9, (i) no, (ii) no
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48 An automobile company has two factories, and each factory makes the same three models of car. At α = 0.05, find the test values FA , FB. Is there any difference in the mean mileage depending on the (i) factory (ii) type of model using a two-way ANOVA.[ A : Factory and B : Type of model ]
A ) 13.09, 32.3, (i) no, (ii) yes
B ) 4.7, 3.9, (i) yes, (ii) yes
C ) 13.09, 32.3, (i) yes, (ii) yes
D ) 4.7, 3.9, (i) no, (ii) no
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49 There are three groups of plants that were exposed to 8 hours,12 hours and 16 hours of sunlight per day during a given growing period and two kinds of fertilizers (P and Q) were used. The heights of the plants(in feet) after six month are tabulated as follows. At α = 0.05, find the test values FA , FB. Is there any difference in the mean height of plants depending on the (i) type of fertilizer (ii) duration of exposure to sun using a two-way ANOVA.[ A : Fertilizer and B : Exposure to sun ]
A ) 4.7, 3.9, (i) no, (ii) no
B ) 30.08, 64.03, (i) no, (ii) no
C ) 30.08, 64.03, (i) yes, (ii) yes
D ) 4.7, 3.9, (i) yes, (ii) yes
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50 There are three groups of plants that were exposed to 8 hours,12 hours and 16 hours of sunlight per day during a given growing period and two kinds of fertilizers (P and Q) were used. The heights of the plants(in feet) after six month are tabulated as follows. At α = 0.05, find the test values FA , FB. Is there any difference in the mean height of plants depending on the (i) type of fertilizer (ii) duration of exposure to sun using a two-way ANOVA.[ A : Fertilizer and B : Exposure to sun ]
