A borrower that fails to make payments on their loan is said to be delinquent. T

Question

A borrower that fails to make payments on their loan is said to be delinquent. The proportion of delinquent borrowers is called the delinquency rate. Federal regulators want to use a 95% confidence interval to estimate the true difference in the delinquency rates for two types of loan: conventional home loans and home loans insured by the Federal Housing Administration. (They subtract in the order pFHApconventional {"version":"1.1","math":"p_ ext{FHA} - p_ ext{conventional}"}.) Based on data obtained from a random sample, their confidence interval is (0.041, 0.053). Which one of the following is the best way to report this confidence interval? (Assume the requirements for this confidence interval are met.) 1)We are 95% confident that the true difference in the delinquency rates is between 0.041 and 0.053. 2)We are 95% confident that the difference between the sample delinquency rates is between 0.041 and 0.053. 3)We are 95% confident that the true delinquency rate is between 0.041 and 0.053. 4)We are 95% confident that the data lie between between 0.041 and 0.053. which is it?

Explanation / Answer

If repeated samples were taken and the 95% confidence interval computed for each sample, 95% of the intervals would contain the population mean. ... It is natural to interpret a 95% confidence interval as an interval with a 0.95 probability of containing the population mean.

A option is right.

We are 95% confident that the true difference in the delinquency rates is between 0.041 and 0.053.

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