# Determining credit worthiness

1. Credit card companies use a scoring model to determine the credit worthiness of a prospective card holder. Factors such as income, employment, home ownership, and credit history determine one's score. Suppose an economist, interested in the current cutoff score used by financial institutions, randomly sampled 44 issuers and obtained the following scores.

643 640 630 635 632 641 641 639 641 637 646

638 636 635 629 630 638 641 633 634 636 638

647 635 638 632 634 644 635 637 632 636 640

633 640 639 630 636 642 638 643 633 631 635

a. For this study, what is the variable of interest? What is the population this data is taken from? Explain.

b. Find the sample mean and standard deviation for this data set. Record those below.

c. What does the sample mean represent in the context of this problem? Please be specific.

d. Create a 95% confidence interval for this data set. Show your work and indicate the interval below.

e. Interpret this interval in the context of the problem. Please specifically address what our variable represents and the confidence level.

f. Do you think a 99% confidence interval for this same data set would be wider or narrower than the 95% confidence interval? Explain.

g. Create a 99% confidence interval for this data set. Show your work and indicate the interval below.

h. Interpret this interval in the context of the problem. Please specifically address what our variable represents and the confidence level.

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#### Solution Preview

a. The variable of interest in this problem is the cutoff credit score used by financial institutions. The sample of credit scores from 44 issuers came from the population of all cutoff credit scores from all issuers.

Please see the attached document for b).

c. The sample mean is ...

#### Solution Summary

The credit worthiness is determined. The interest for the current cutoffs are calculated.