Question

10)

An FTC agent is investigating a payday loan service. The agent reviews the records for 112 people who had borrowed money from the lender, and found that 28 of these individuals had defaulted on their loan.

a) Find a 95% confidence interval for the true proportion of borrowers from the service who defaulted on their loans.

b) Provide the margin of error of the interval as your answer.

Round your answer to 4 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 0.25

1 - = 1 - 0.25 = 0.75

Z/2 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.25 * 0.75) /112 )

= 0.0802

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.25 - 0.0802 < p < 0.25 + 0.0802

0.1698 < p < 0.3302

The 95% confidence interval for the population proportion p is : 0.1698 , 0.3302