Question

Erin O'Brien, Director of Consumer Credit with Auckland First Bank (AFB), has implemented a 'fast feedback' to keep her informed of the default rate on personal loans at AFB member banks. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The 90% confidence interval for the population proportion is _________. Select one: a. 0.046 to 0.074 b. 0.039 to 0.081 c. 0.043 to 0.077 d. 0.028 to 0.060

Answer 1

Solution :

Given that,

n = 500

x = 30

= x / n =30 / 500 = 0.060

1 - = 1 - 0.060 = 0.940

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.060 * 0.940 ) / 500 )

= 0.017

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.060 - 0.017 < p < 0.060 + 0.017

0.043 < p < 0.077

The 90% confidence interval for the population proportion p is : ( 0.043 , 0.077)

Answer c ) is correct.