Question

A local bank has set a goal of limiting default rates on its new home mortgage loans to less than 18 percent. After implementing new mortgage loan screening and approval processes for the last five years, the management randomly selected 200 home mortgage loans extended over the last five years and discovered that 24 of these loans were in default. Based on the given evidence, please construct and interpret the 99% 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

H0: mu = 0.44
Ha: mu < 0.18

sample proportion, pcap = 24/200 = 0.12
sample size, n = 200
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.12 * (1 - 0.12)/200) = 0.023

For 0.99 Confidence level, the z-value = 2.58
CI = (xbar - z*SE, xbar + z*SE)
CI = (0.12 - 2.58 * 0.023 , 0.12 + 2.58 * 0.023)
CI = (0.0607 , 0.1793)

As the above CI does not include 0.18, we reject H0
There are significant evience to conclude that the bank is achieving its stated goal.