credit, card represents, a line of credit, bęcause the the card is used to pay for a purchase. 'A studyOFCrediFar ECAOlder Obtains a 9RRWheneve card accounts opened in card holder tăt the time the card waş issued).of 731 and a standard DřiscolL Xayier Gapaix, and David Caibson, mean, FICO Score forhe SimitAgarwal, John, deviation of (6. TSource: "Learning in the Credit Card Market,"Wörking Paper 13822, National Buřeau of Economic Research (NBER), Febrüary 2008.] You conduct a hypothesis test to determine whether bạnks have Josened their standards for issuing credt cards since 2002 You ES'ECTA past 6 months. The sample mean were issued) is x = 717. Assume that the standard deviation of the population of FICO scores for gredit cards issued during the past 6 months is known to be o = 76, the standard deviation from the NBER study. a rangom sample of the credit cărd KoidaeaE Fards issued during the (at the timẽ their cards
credit, card represents, a line of credit, bęcause the the card is used to pay for a purchase. 'A studyOFCrediFar ECAOlder Obtains a 9RRWheneve card accounts opened in card holder tăt the time the card waş issued).of 731 and a standard DřiscolL Xayier Gapaix, and David Caibson, mean, FICO Score forhe SimitAgarwal, John, deviation of (6. TSource: "Learning in the Credit Card Market,"Wörking Paper 13822, National Buřeau of Economic Research (NBER), Febrüary 2008.] You conduct a hypothesis test to determine whether bạnks have Josened their standards for issuing credt cards since 2002 You ES'ECTA past 6 months. The sample mean were issued) is x = 717. Assume that the standard deviation of the population of FICO scores for gredit cards issued during the past 6 months is known to be o = 76, the standard deviation from the NBER study. a rangom sample of the credit cărd KoidaeaE Fards issued during the (at the timẽ their cards
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Question
![5. Testing the population mean when the population standard deviation is known
Lenders tighten or loosen their standards for issuing credit as economic conditions.change. One of
the criteria Tenders use to evaluate the creditworthinesS of a potential borroWer.js her credit risk
Score, usually.a FICO Score. FICO Scores range from 300 to 850. A consumer with a high|
Score is perceived to be a low credīt risk to the lėňdeř ăňd is more likelý to be extended' cređiť than
à consumér with a low score.
A credit, card represents, a line of credit,,bęcause the credit card holder obtains a loan whenever
the card
mean FICO score for the credit card holder at the time the card was issued) of
deviation of 76. TSource: Sumit Agārwal John C. DriscoLXayier Gabaix, and David Laibson
Learning in the Credit Card Märket," "Wörking' Paper 13822, National Buřeau of Economič Research
(NBER), Fébrüary 2008.]
used to paY for a purchase. A study of creditcard accounts opened in 2002 found a
[731 and a standard
You conduct a hypothesis test to determine whether bạnks have Josened their standards for
ISsuing credit cards since 2002. You collect a rangom sample of 64 credit cards ISsued during the
past 6 montis. The sample mean FICO Score of the credit cărd holders (at the time their cards
were issued) is x = 717. Assume that the standard deviation of the population of FICO scores for
gredit cards issued during the past 6 months is known to be o =
the NBER Study.
76, the standard deviation from
Let H equal the true population mean, FICO score for.consumers issued credit cards in the past 6
months. You should formulate the nüll' ând ălterňative hypotheses as:
O Ho: x =
731, H1: x < 731
Ho: μ -731, Η 1: μ < 731
Ho: µ < 731, H1: µ = 731
Ho: µ = 731, H1: µ > 731
If the null hypothesis is true as an equality, the sampling distribution of x is approximated by
and a standard deviation of
distribution with
The value of the standardized test statistic is
Use the Distributions tool to help you answer the questions that follow.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b714a0e-b01f-49d4-9d2a-b07b3adf1f36%2F92db774e-122d-4f13-ba4a-8c523244ef58%2F6tkpcur_processed.png&w=3840&q=75)
Transcribed Image Text:5. Testing the population mean when the population standard deviation is known
Lenders tighten or loosen their standards for issuing credit as economic conditions.change. One of
the criteria Tenders use to evaluate the creditworthinesS of a potential borroWer.js her credit risk
Score, usually.a FICO Score. FICO Scores range from 300 to 850. A consumer with a high|
Score is perceived to be a low credīt risk to the lėňdeř ăňd is more likelý to be extended' cređiť than
à consumér with a low score.
A credit, card represents, a line of credit,,bęcause the credit card holder obtains a loan whenever
the card
mean FICO score for the credit card holder at the time the card was issued) of
deviation of 76. TSource: Sumit Agārwal John C. DriscoLXayier Gabaix, and David Laibson
Learning in the Credit Card Märket," "Wörking' Paper 13822, National Buřeau of Economič Research
(NBER), Fébrüary 2008.]
used to paY for a purchase. A study of creditcard accounts opened in 2002 found a
[731 and a standard
You conduct a hypothesis test to determine whether bạnks have Josened their standards for
ISsuing credit cards since 2002. You collect a rangom sample of 64 credit cards ISsued during the
past 6 montis. The sample mean FICO Score of the credit cărd holders (at the time their cards
were issued) is x = 717. Assume that the standard deviation of the population of FICO scores for
gredit cards issued during the past 6 months is known to be o =
the NBER Study.
76, the standard deviation from
Let H equal the true population mean, FICO score for.consumers issued credit cards in the past 6
months. You should formulate the nüll' ând ălterňative hypotheses as:
O Ho: x =
731, H1: x < 731
Ho: μ -731, Η 1: μ < 731
Ho: µ < 731, H1: µ = 731
Ho: µ = 731, H1: µ > 731
If the null hypothesis is true as an equality, the sampling distribution of x is approximated by
and a standard deviation of
distribution with
The value of the standardized test statistic is
Use the Distributions tool to help you answer the questions that follow.
Transcribed Image Text:Use the Distributions tool to help you answer the questions that follow.
Normal Distribution
Mean = 730
Standard Deviation =
8.5
710
720
730
740
75(8
-2
-1
1
2
You conduct the hypothesis test using a şignificance leVEL SDproach, when do you reject the ňll
of
Use the tool to develop the.
rejection region for"yoür test. According to the critical value
hypothesis?
O Reject H1 if z < -1.282
o Reject Ho if z < -1.645 or z 2 1.645
o Reject H, if z < -1.282
o Reject H, if z 2 -1.47
The p-value is
Using the critical value approach, the null hypothesis is
because
Using the p-value approach, the null hypothesis is
because
their standards for issutng credit cards since 2002.
Therefore, you
conclude that banks have loosened
Expert Solution
Step 1
Part 1: Given: , ,
According to the given information, the hypothesis of interest is
H0:
H1:
Under the null hypothesis, the sampling distribution of is approximated by the normal distribution with mean and standard deviation = 9.5
The value of the standardized test statistic is:
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