5. Testing the population mean when the population standard deviation is known 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 scorer usually a FICD score. FICD 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 creditr 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 II'E. [Source: Sumit Agarwal, John C. Driscoll, Xavier Gabai):r and David Laibsonr "Learning in the Credit Card Marketr" Working Paper 13822. National Bureau of Economic Research (NBER), February 2005.] 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 i = T49. Assume that the standard deviation of the population of FICD scores for credit cards issued during the past 6 months is known to be cs = 76r the standard deviation from the NBER study. You conduct the hypothesis test using a significance level of a = 0.05. Use the tool to develop the rejection region for your test. According to the critical value approach, when do you reject the null hypothesis? O Reject Ho if z 2 1.645 Reject Ho if z $ 1.89 O Reject H1 if z 2 1.645 O Reject Ho if z $ -1.96 or z 2 1.96 The p-value is Using the critical value approach, the null hypothesis is , because 7 . Using the p-value approach, the null hypothesis is because . Therefore, you conclude that banks have tightened their standards for issuing credit cards since 2002