Question

Find a data set on the internet. Some suggested search terms: Free Data Sets, Medical Data Sets, Education Data Sets.

1. Introduce your Data Set and Cite the Source.
2. What trends do you notice in your data set?
3. Based on the trends and the history of your data set, make a claim. What kind of test (left, right, two tailed) would you have to complete?
4. Explain the steps needed to complete the Hypothesis Test. What is needed?

Answer 1

We have obtained the data set on monthly road accidents in Uttar Pradesh for the past 14 years (2001-2014) and therefore there are 168 data points.
Below is the link of our data:
https://www.kaggle.com/pratimtalukdar/road-accidents-in-indian-states-2001-2014

Information of our Data:
Head of the data : ##Monthly Road Accidents in Uttar Pradesh(2001-2014)

January 2001 1695

February 2001 1737

March 2001 1652

April 2001 1663

May 2001 1733

June 2001 1027
Tail of the Data ##Monthly Road Accidents in Uttar Pradesh(2001-2014)

January 2014 2086

February 2014 2017

March 2014 1824

April 2014 2023

May 2014 2170

June 2014 2325
Summary of the Data ##Monthly Road Accidents in Uttar Pradesh(2001-2014)

Min 794

1st Quantile 1248

Median 1628

Mean 1634

3rd Quantile 2031

Max 2554

Checking Presence of Trend and Seasonality in the data Testing of Presence of Trend in the model:
We have to check if there is a trend in the model or not.
Relative Ordering test is conducted.
H0 : No Trend in the model.
against H1 : Trend is present in the model. R: Number of discordant pairs ?(?)=?(?−1)/4
If R > E(R): indication of falling trend
R < E(R): indication of rising trend.
R is related with Kendell’s (τ), the rank correlation coefficient. ?=1−{4?/?(?−1)}
Under H0, E(τ) = 0 ?ar(?)=2(2?+5)/9?(?−1)

Test statistic: ?=(?−?(?))/???(?) ~ ?(0,1)
Test Criterion:
Reject H0 if observed |Z|>Zα/2 at α level of significance.
Value of R =2613, E(R)=7014. There is rising trend in our model.
|Z|=12.07334 >1.96(Z0.025), and hence we reject our null hypothesis.
We conclude that there is presence of trend in the model.

R-Codes
####----Time Series Analysis of Road Accidents in Uttar Pradesh----####
getwd()
up <- read.csv(choose.files())
attach(up)
head(up)
tail(up)
summary(up)
up1 = ts(up, start = c(2001, 1), end = c(2014, 12), frequency = 12)
D = decompose(up1)
plot.ts(up1, ylab = "Monthly Road Accidents in Up (2001-2014)", xlab = "Years")
plot(D)
#------Test for Randomness(Turning pt. test)--------#
#------Null hypothesis-Series is purely random------#
tp_tst = function(y)
{ q_ij = 0
for(i in 2:(length(y)-1))
{
if(((y[i] > y[i+1])&&(y[i] > y[i-1])) || ((y[i] < y[i+1])&&(y[i] < y[i-1])))
q_ij = q_ij + 1
}
cat(q_ij)
exp_T = (2/3)*(length(y)-2)
V_T = (16*length(y)-29)/90
tst_stat = (q_ij-exp_T)/sqrt(V_T)
cat(tst_stat)
z_alpha=qnorm(0.025)
if(abs(tst_stat) > abs(z_alpha))
{
cat(" \n On the basis of the given data Null Hypothesis is rejected")
}
else
{
cat(" (On the basis of the given data Null Hypothesis is accepted)")
}
}
tp_tst(racci)
####-----checking presence of trend (Relative Ordering Test)-----####
####-----------------Null Hypothesis-No trend--------------------####