Question

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 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 loosened their standards for issuing credit cards since 2002. You collect a random sample of 100 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 - 717. Assume that the standard deviation of the population of FICO scores for credit cards issued during the past 6 months is known to beo - 76, the standard deviation from the NBER study, Let u 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 Hop - 731, H:p> 731 Họ: || 731, H1: H = 731 ****

Answer 1

Solution:

hypotheses as: O Ho: p = 731, H1: p > 731 O Ho: p < 731, H1: p = 731 O Ho: p = 731, H1: p < 731 O Ho: X - 731, H1:1 < 731 4 = 731 normal distribution If the null hypothesis is true as an equality, the sampling distribution of x is approximated by distribution with 731 7.6 and a standard deviation of 717-731 The value of the standardized test statistic is -1.842 Z= = -1.842 7.6 76 Tn 1100 = X-4 = 7.6 vn

You conduct the hypothesis test using a significance level of a -0.10. Use the tool to develop the rejection region for your test. According to the critical value approach, when do you reject the null hypothesis? Reject Ho if zs -1.282 O Reject He if zs -1.645 or z 2 1.645 O Reject H, if zs -1.282 O Reject He if z > -1.84 The p-value is 0.0327 The excel function to find the p-value is: -NORMSDIST(-1.842) Z< -1.282 Using the critical value approach, the null hypothesis is rejected because Using the p-value approach, the null hypothesis is rejected because p-value <0.10 Therefore, you should conclude that banks have loosened their standards for Issuing credit cards since 2002 Grade It Now Save & Continue Continue without saving