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 x̄x̄ = 715. Assume that the standard deviation of the population of FICO scores for credit cards issued during the past 6 months is known to be σ = 76, the standard deviation from the NBER study. Let µ 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: H₀: µ = 731, H11 : µ < 731 H₀: µ = 731, H11 : µ > 731 H₀: x̄x̄ = 731, H11 : x̄x̄ < 731 H₀: µ < 731, H11 : µ = 731 If the null hypothesis is true as an equality, the sampling distribution of x̄x̄ is approximated by selector 1
The value of the standardized test statistic is selector 1
Use the Distributions tool to help you answer the questions that follow. Normal Distribution Mean = 730 Standard Deviation = 8.5
Reject H1 if z ≤ –1.645 Reject H₀ if z ≥ –2.11 Reject H₀ if z ≤ –1.645 Reject H₀ if z ≤ –1.96 or z ≥ 1.96 The pvalue is selector 1
Using the critical value approach, the null hypothesis is selector 1

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