Question

# Lenders tighten or loosen their standards for issuing credit as economic conditions change. One of the...

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 x̄x̄ = 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 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, Haa: µ > 731

H₀: µ > 731, Haa: µ ≤ 731

H₀: x̄x̄ ≤ 731, Haa: x̄x̄ > 731

H₀: µ ≥ 731, Haa: µ < 731

If the null hypothesis is true as an equality, the sampling distribution of x̄x̄ is approximated bya normal   distribution witha mean of 731   and a standard deviation of9.5   .

The value of the standardized test statistic isz = 1.58   .

Normal Distribution

Mean = 730

Standard Deviation = 8.5

710720730740750x̄z-2-1012z

You conduct the hypothesis test using a significance level of α = 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 H₀ if z ≤ 1.58

Reject H₀ if z ≥ 1.282

Reject Haa if z ≥ 1.282

Reject H₀ if z ≤ –1.645 or z ≥ 1.645

The p-value is0.0571   .

Using the critical value approach, the null hypothesis isnot rejected   , because   . Using the p-value approach, the null hypothesis isnot rejected   , because   . Therefore, youcannot   conclude that banks have tightened their standards for issuing credit cards since 2002.

Similar to this problem just different numbers

1)

H₀: µ ≤ 731, Haa: µ > 731

 sample mean 'x̄= 746 sample size    n= 64 std deviation σ= 76 std error ='σx=σ/√n= 9.5 test stat z = '(x̄-μ)*√n/σ= 1.58
 Decision rule:reject Ho if test statistic z>1.282
 p value        = 0.0571

Using the critical value approach, the null hypothesis is rejected because    test staitsitc is higher than critical value

Using the p-value approach, the null hypothesis is rejected because p value is less than 0.10

Therefore, you can onclude that banks have tightened their standards for issuing credit cards since 2002.

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