Question

PLEASE USE R PROGRAMMING TO SOLVE THIS AND GIVE A COPYABLE CODE

Professor David teach Math 1054. In that course, there are 5 exams, 4 midterm exams, plus final exam. You are asked to help him to check whether there is significant difference among the difficulty level in these 5 exams. The data is stored in Math1054Exam.txt.

a). read in data (copy your R code)

b). Find averages for these exams. You can use mean(V) function, or summary(data) function.

c). Are these averages differ significantly? We need to use ANOVA. For this purpose, you need to use stack function to change the data format as two column, one is score, the

other is exam index.

d). Produce a boxplot for the five exams.

e). Conduct ANOVA test.

f). Copy your ANOVA table.

g). Make your conclusion.

------------------------------------------------------------------------------4

Math1054Exam.txt.

T1   T2   T3   T4   Final
90   69   62   65   92
67   59   78   63   43
76   73   66   41   71
80   92   46   92   70
98   79   60   84   99
82   80   69   83   94
69   45   47   70   37
83   90   54   66   50
93   94   90   94   99
66   67   50   52   32
45   71   55   58   83
76   92   65   72   95
73   92   84   70   77
81   68   30   53   34
60   58   43   50   36
92   90   86   89   95
62   54   52   60   88
85   80   65   82   88
69   80   81   67   75
71   88   43   61   89

Answer 1

data =read.table("../Documents/Tutoring/Software/random data/exam.txt",header =T)

#b
sapply(data, mean)
#c
sData<- stack(data)
model <- aov( values~ind , sData)
summary(model)

#d
boxplot(data)

b)

c)

p-value = 0.0414 < alpha (0.05)

hence we reject the null hypothesis

we conclude that there is significant difference

d)

e)

p-value = 0.0414 < alpha (0.05)

hence we reject the null hypothesis

we conclude that there is significant difference

f)

           Df Sum Sq Mean Sq F value Pr(>F)  
ind          4   3021   755.3   2.593 0.0414 *
Residuals   95  27672   291.3                 
---

g)

p-value = 0.0414 < alpha (0.05)

hence we reject the null hypothesis

we conclude that there is significant difference

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