Question

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   .

Use the Distributions tool to help you answer the questions that follow.

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.

https://www.chegg.com/homework-help/questions-and-answers/lenders-tighten-loosen-standards-issuing-credit-economic-conditions-change-one-criteria-le-q19797498

Similar to this problem just different numbers

Answer 1

1)

H₀: µ ≤ 731, Haa: µ > 731

sample mean 'x̄=	746.000
sample size    n=	64.00
std deviation σ=	76.000
std error ='σx=σ/√n=	9.5000
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.