Question

A questionnaire was sent out to students of a certain college to find out who is responsible for paying their fees. The researcher found that 30 out of 100 students pay their own fees. Create a 90% confidence interval of the proportion of students who pay their own fees.

Answer 1

let us consider the x is the no of students who pay their own fees is 30

and n is the total no of students =100

The sample proportion is p̂ and

p̂ = 30/100 =0.3

the confidence interval can be computed with this formula:

where the standard error of the point estimate is:

hence   = 0.30.075 = (0.225,0.375)

90% confidence interval of the proportion of students who pay their own fee is (0.225,0.375)