Question

A local bank has set a goal of limiting default rates on its new home mortgage loans to less than 20 percent. After implementing new mortgage loan screening and approval processes for the last five years, the management randomly selected 100 home mortgage loans extended over the last five years and discovered that 13 of these loans were in default. Based on the given evidence, please construct and interpret the 90% confidence interval for the population proportion of home mortgage loans that are in default for this bank. According to your results, do you think the bank is achieving its stated goal? Please justify your answer.

Answer 1

Sample proportion = 13 / 100 = 0.13

90% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.13 - 1.645 * sqrt( 0.13 * 0.87 / 100) < p < 0.13 + 1.645 * sqrt( 0.13 * 0.87 / 100)

0.075 < p < 0.185

90% CI is ( 0.075 , 0.185)

Interpretation -

We are 90% confident that population proportion of the home mortgage loan that are default for this bank is between

0.075 and 0.185

Conclusion -

Since all values in the confidence interval are less than 0.20, we conclude that the bank achieving its stated goal.