In a news story distributed by the Washington Post , it was reported that a subs

Question

In a news story distributed by the Washington Post, it was reported that a substantial fraction of mortgage loans that go into default within the first year of the mortgage were approved on the basis of falsified applications. For instance, loan applicants often overstate their income or fail to disclose all of their debts.

Suppose that a random sample of 1,000 mortgage loans that defaulted within the first year reveals that 410 of these loans were approved on the basis of falsified information.

What is the Lower Confidence Limit (LCL) of the 95% confidence interval for the proportion of all first-year defaults that were approved on the basis of falsified applications? Include 3 decimal places in your answer.

Explanation / Answer

n = 1000

x = 410

p = 410/1000

p = 0.41

q=1- 0.41

q = 0.59

SD = sqrt(pq/n)

SD = sqrt(( 0.41*0.59 )/1000)

SD = sqrt(0.0002419)

SD = 0.0156

Z0.05 = 1.96

Lower Confidence Limit (LCL) of the 95% confidence interval for the proportion of all first-year defaults that were approved on the basis of falsified applications,

LCL =(xbar - Z0.05 * SD)

=(0.41 - (1.96*0.0156))

LCL = 0.380

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