Question

The data frame TestScores in the PASWR packages gives the test grades of 20 students taking a basic statistic course.

a) Use the function EDA() on the data. Can normality be assumed?

b) Perform the test for normal distribution.

Use R to solve and show R code

Answer 1

a)

> library(PASWR)
> Data=TestScores[1:20,]
> EDA(Data)
[1] "Data"
Size (n) Missing Minimum 1st Qu Mean Median TrMean 3rd Qu Max. Stdev.
20.000 0.000 57.000 68.000 75.200 76.000 75.278 82.500 92.000 9.507
Var. SE Mean I.Q.R. Range Kurtosis Skewness SW p-val
90.379 2.126 14.500 35.000 -0.842 -0.097 0.938

From above graph we can say that grades of 20 students is normally distributed.

b)

> library(nortest)

i) Shapiro-Francia test for normality

Hypothesis,

H₀= Grades of 20 students is normally distributed

H₁=Grades of 20 students is not normally distributed

> sf.test(Data)

Shapiro-Francia normality test

data: Data

W = 0.9865, p-value = 0.9681

Here p-value > alpha=0.05

therefore we accept the H₀

Therefore we can say that grades of 20 students is normally distributed.

ii)Anderson-Darling test for normality

Hypothesis,

H₀= Grades of 20 students is normally distributed

H₁=Grades of 20 students is not normally distributed

> ad.test(Data)

Anderson-Darling normality test

data: Data

A = 0.17194, p-value = 0.9173

Here p-value > alpha=0.05

therefore we accept the H₀

Therefore we can say that grades of 20 students is normally distributed.