Bank Loans

Find a 90% confidence interval for the difference in population mean credit scores for those approved and those denied bank loans, using the data in Table 10.

Solution

Both sample sizes are large (), so we may construct the interval. For , the required degrees of freedom is the smaller of and , which is . Because is not listed in the table, we use the next lower value listed as a conservative alternative: . For 90% confidence, then .

The margin of error is

The 90% confidence interval is then

We are 90% confident that the difference in population mean credit scores lies between 60.066 and 85.934. Because 0 is not contained in this interval, we may conclude that , just as we did in Example 8.

Exercises 11–16.