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

 

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

.

Problem:

Random samples of 400 men and 600 women asked whether they would like to have a fly over near

their residence. 200 men and 325 women were in favour of it. Test the equality of men and women

in the proposal.

R – Code:-

The null hypothesis H0: p1=p2

Alternate hypothesis H1: proportions are different

We begin with computing the test statistic.

> n1=400

# Sample1 size

> p1=200/n1

# Sample1 proportion

> n2=600

# Sample2 size

> p2=325/n2

# Sample2 proportion

> P=(n1*p1+n2*p2)/(n1+n2)

> Q=1-P

> z=abs((p1-p2)/sqrt(P*Q*(1/n1+1/n2)))

> z

# test statistic

[1] 1.292611

>alpha=0.05

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

>z.alpha # critical value

[1] 1.959964