Lenders tighten or loosen their standards for issuing credit as economic conditions change. One of the criteria lenders use to evaluate the creditworthiness of a potential borrower is her credit risk score, usually a FICO score. FICO scores range from 300 to 850. A consumer with a high FICO score is perceived to be a low credit risk to the lender and is more likely to be extended credit than a consumer with a low score.

A credit card represents a line of credit, because the credit card holder obtains a loan whenever the card is used to pay for a purchase. A study of credit card accounts opened in 2002 found a mean FICO score for the credit card holder (at the time the card was issued) of 731 and a standard deviation of 76. [Source: Sumit Agarwal, John C. Driscoll, Xavier Gabaix, and David Laibson, "Learning in the Credit Card Market," Working Paper 13822, National Bureau of Economic Research (NBER), February 2008.]

You conduct a hypothesis test to determine whether banks have tightened their standards for issuing credit cards since 2002. You collect a random sample of 64 credit cards issued during the past 6 months. The sample mean FICO score of the credit card holders (at the time their cards were issued) is x?x?= 746. Assume that the standard deviation of the population of FICO scores for credit cards issued during the past 6 months is known to be ? = 76, the standard deviation from the NBER study.

A, Let equal the true population mean FICO score for consumers issued credit cards in the past 6 months. You should formulate the null and alternative hypotheses as:

a,H?: = 731, H11:

b,H?: x?x?= 731, H11: x?x?> 731

c,H?: = 731, H11: > 731

d, H?: > 731, H11: = 731

B, If the null hypothesis is true as an equality, the sampling distribution of x?x?is approximated by a, a bionminal b, a normal c, a standard normal d t e,an unknown distribution with a an unknoown b, a mean of 0 c, a mean of 746 d, a mean of 731 and a standard deviation of a 1.0 b, 9.5 c, 76 d, unknowm .

The value of the standardized test statistic is .a, z=15 b z=746 c, t = 1.58 d z= 1.58

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