Question

A survey of 16 randomly chosen students, 2 of them have a surfing board. Create a 90% confidence interval for the proportion of students who have a surfing board based on the survey. Please find the upper limit using R.

Answer 1

Ans. 90% confidence interval using R

> n=16
> x=2
> p=x/n
> p
[1] 0.125
> #90% Confidence interval for P
> alpha=0.10
> #criticalvalue(Z_alpha/2)
> criticalvalue=qnorm((alpha/2),0,1,lower.tail=F)
> criticalvalue
[1] 1.644854
> #Margin of error(E)
> E=criticalvalue*sqrt(((p*(1-p))/n))
> E
[1] 0.1359961
> LowerLimit=p-E
> LowerLimit
[1] -0.01099605
> UpperLimit=p+E
> UpperLimit
[1] 0.2609961