2. Hypothesis tests about a population mean, population standard deviation 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 x̄ x̄ = 722. 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: x̄ x̄ ≥ 731, Haa: x̄ x̄ < 731 H₀: µ < 731, Haa: µ ≥ 731 H₀: µ ≥ 731, Haa: µ < 731 H₀: µ ≤ 731, Haa: µ > 731 If the null hypothesis is true as an equality, the sampling distribution of x̄ x̄ is approximated by _ distribution with_ and a standard deviation of _ . The value of the standardized test statistic is___ . Use the Distributions tool to help you answer the questions that follow. You conduct the hypothesis test using a significance level of α = 0.05. 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 ≤ –1.96 or z ≥ 1.96 Reject Haa if z ≤ -1.645 Reject H₀ if z ≤ -1.645 Reject H₀ if z ≥ -1.18 The p-value is _ . Using the critical value approach, the null hypothesis is , because . Using the p-value approach, the null hypothesis is , because . Therefore, you _ conclude that banks have loosened their standards for issuing credit cards since 2002.

Question

2. Hypothesis tests about a population mean, population standard deviation 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 x̄ x̄ = 722. 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: x̄ x̄ ≥ 731, Haa: x̄ x̄ < 731

H₀: µ < 731, Haa: µ ≥ 731

H₀: µ ≥ 731, Haa: µ < 731

H₀: µ ≤ 731, Haa: µ > 731

If the null hypothesis is true as an equality, the sampling distribution of x̄ x̄ is approximated by _____ distribution with_______ and a standard deviation of _____ .

The value of the standardized test statistic is_________ .

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

You conduct the hypothesis test using a significance level of α = 0.05. 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 ≤ –1.96 or z ≥ 1.96

Reject Haa if z ≤ -1.645

Reject H₀ if z ≤ -1.645

Reject H₀ if z ≥ -1.18

The p-value is _______ .

Using the critical value approach, the null hypothesis is ____ , because ______ . Using the p-value approach, the null hypothesis is ____ , because ____ . Therefore, you _____ conclude that banks have loosened their standards for issuing credit cards since 2002.