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.

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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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