Question

The on-base percentage (OBP) indicates how successful a baseball player is as a batter. The dataset OBP in UsringR contains the OBP for the year 2000. Test whether these data come from normal distribution.

Use R to solve and show R code

Answer 1

#Removing all the variables and libraries
rm(list=ls())

#Loading the required library UsingR
#You can install it using install.packages("UsingR")

library(UsingR)

# We will verify the normality using quantile plot and density plot.
# Loading the dataset

OBP[1:10]
youngdm01 velarra01 tynerja01 thompry01 selbybi01 riverru01 matosju01 maciajo01
0.3287037 0.3246753 0.2485876 0.2945205 0.2784091 0.3021978 0.2791878 0.2943548
maciajo01 lopezlu02
0.2905983 0.2321429

#Now convert the data in a usable format

df <- as.numeric(OBP)
df[1:20]
[1] 0.3287037 0.3246753 0.2485876 0.2945205 0.2784091 0.3021978 0.2791878
[8] 0.2943548 0.2905983 0.2321429 0.2616279 0.3198529 0.3254593 0.3561644
[15] 0.2958580 0.2388060 0.2846154 0.2916667 0.3643725 0.2800000
# Quantile Plot
# qqnorm()function will do this for us

qqnorm(df)

#Now use density plot

plot(density(df))

# We will also use shapiro.test() function to perform Shapiro-Wilk test
# Ho: Data is normal H1: Data is not normal
# If p-value<0.05 Reject null hypothesis otherwise fail to reject null hypothesis

shapiro.test(df)

Shapiro-Wilk normality test

data: df
W = 0.97092, p-value = 1.206e-07

# p-value = 1.206e-07 < 0.05, Hence reject the null hypothesis.
# Our data is not normally distributed
# You can also see in the density plot that it is positively skewed.
# Also in the quantile plot points are not distributed close to the diagonal line.
# Our data is not normally distributed.

*the bold text is output