2. Hypothesis tests about a population main, population standard deviation known Lenders tighten or loosen their standards for issuing credit as economic conditions change. One of the or teris 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 l'kely 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 par for a purchase, A study of credit card accounts opened in 2093 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. [Souror: Sumit Agarwal, John C. Driscoll, Xavier Gabaix, and David Laibson, "Learning in the Credit Card Market," Working Paper 13832, National Bureau of Economic Research (NBER), February 2000.] You conduct a hypothesis best in determine whether banks have tightened their standards for issuing credit cards ance 20 03, You collect a random sample of $4 credit cards issued during the past 6 months, The simple mean FCD score of the credit card holders (at the time their cards were issued) is * = 745, Assume that the standard deviation of the population of FOCO scores for credit cards issued during the past & months is known to be a = 70, the standard deviation from the Neck study. Let pi 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: O Heg i s 791, H : 8 > 731 Heyp 2 731, Hip 731 If the null hypothesis is true as an aquality, the sampling distribution of $ is approximated by distribution with and a standard deviation of The value of the standard and best statistic is Use the Distributions beal to halp you answer the questions that follow. Standard Drain - IF 80 0 ANA You conduct the hypothesis best using a s'one cance level of a = .10. Use the tool to develop the rejection repon for your best. According to the critical value approach, when do you reject the null hypothesis? O Reject H Ez s -1.645 or z 2 1.645 Q Reject My 1 2 2 1.282 O Reject H 1 2 5 147 O Reject H, 1/ 2 2 1.282 The p-value is Using the critical valve approach, the null hypothesis is . 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