To test whether there is significant difference between two sample means using R language

 

Aim: To test whether there is significant difference between two sample means.

Problem:

A college conduct both day and night classes intended to be identical. A sample of 100 day

students yields examination results as

and a sample of 200 night students

as

. Are the two means statistically equal at 5% level?

R code:-

The null hypothesis H0 ,

Alternative hypothesis H1 ,

We begin with computing the test statistic.

> x1bar=72.4

# Sample1 mean

> x2bar=73.9

# Sample2 mean

> s1=14.8

# Sample1 SD

> s2=17.9

# Sample2 SD

> n1=100

# Sample1 size

> n2=200

# Sample2 size

> Test_Statistics=abs(((x1bar-x2bar)/sqrt((s1^2/n1)+(s2^2/n2))))

> Test_Statistics

[1] 0.7702493

We then compute the critical value at .05 significance level.

>alpha=0.05

>z.alpha=qnorm(1-alpha/2)

> z.alpha

[1] 1.959964