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 creditworthimess of a potential borrower.js her credit risk usually.a FICO Score. Scores range from 300 to 850. A consumer with a high FICO Score'is perceiyed to be a low credđĩť risk to thě lėňdeř ăñd is more likely to be 'extended' créđiť than a consumer with a loW Score. A credit, card represents, a line of credit,, bęcause the credit card holder obtains a loan whenever the card is used to pay for a purchase. A study of credit card accounts opened in2002 found'a mean FICO Score for the credit card holder (ať the time the card was Issued) of 731 and a standar of 76. ISource: Sumit Agarwar, John C. DriscoL Xayier Gapaix, and Dávid Caibson *Learning in the Credit Card Market,"Wörking Paper 13822, National Buřeau of Economic Research (NBER), Fébrüary 2008.] iSsuing credit cards since past 6 months. The sample mean FICO were issued) is x = 717. Assume that the standard deviation of the population of FICO scores for gredit cards isued during the past 6 months is known to be o = 76, the standard deviation from You.conduct a hypothesis 2002.You collecte of the credit čārd holdérs (at thể time their cards ta determine whether banks have Joosened their standards for a random sample of credit cards ISsued during the study. Let Hegual the months. Yöu should formulate the nuirang SFore for consumers issued credit cards in the past 6 true population mean FICO ānd ălternátive hypöthéses as: O Ho: x = 731, H1: x < 731 Ο H0: μ731, Η ι1: μ < 731 Ο Ho: μ < 731 , Η 1: μ = 731 O Ho: H = 731, Η1: μ> 731 If the null hypothesis is true as an equality, the sampling distribution of x is approximated by a normal 9.5 distribution with a mean of 731 and a standard deviation of The value of the standardized test statistic is z = -1.47 Use the Distributions tool to help you answer the questions that follow.
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 creditworthimess of a potential borrower.js her credit risk usually.a FICO Score. Scores range from 300 to 850. A consumer with a high FICO Score'is perceiyed to be a low credđĩť risk to thě lėňdeř ăñd is more likely to be 'extended' créđiť than a consumer with a loW Score. A credit, card represents, a line of credit,, bęcause the credit card holder obtains a loan whenever the card is used to pay for a purchase. A study of credit card accounts opened in2002 found'a mean FICO Score for the credit card holder (ať the time the card was Issued) of 731 and a standar of 76. ISource: Sumit Agarwar, John C. DriscoL Xayier Gapaix, and Dávid Caibson *Learning in the Credit Card Market,"Wörking Paper 13822, National Buřeau of Economic Research (NBER), Fébrüary 2008.] iSsuing credit cards since past 6 months. The sample mean FICO were issued) is x = 717. Assume that the standard deviation of the population of FICO scores for gredit cards isued during the past 6 months is known to be o = 76, the standard deviation from You.conduct a hypothesis 2002.You collecte of the credit čārd holdérs (at thể time their cards ta determine whether banks have Joosened their standards for a random sample of credit cards ISsued during the study. Let Hegual the months. Yöu should formulate the nuirang SFore for consumers issued credit cards in the past 6 true population mean FICO ānd ălternátive hypöthéses as: O Ho: x = 731, H1: x < 731 Ο H0: μ731, Η ι1: μ < 731 Ο Ho: μ < 731 , Η 1: μ = 731 O Ho: H = 731, Η1: μ> 731 If the null hypothesis is true as an equality, the sampling distribution of x is approximated by a normal 9.5 distribution with a mean of 731 and a standard deviation of The value of the standardized test statistic is z = -1.47 Use the Distributions tool to help you answer the questions that follow.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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![mean FICO Score for the credit card holder (at the time the card waş issued),9ávið Láibson,
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 FICO
Score is perceived to be a low crediť risk to thě léňdeř andď is more likely to be extended' credit than
a consurmēr with a TOw Score.
A credit, card represents, a line of credit,,bęcause 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
731 and a standard
deviation of (6. TSource: Sumit Agarwar, John C. DriscoL Xayier Gapaix, and
Learning in the Credit Card Market,"Wörking Paper 13822, Nätional Büřeau of Economic Research
(NBER), Fébrüary 2008.]
You .conduct a hypothesis
ISsuing credit cards since 26028Atermune whether banks have loosened their standards for
You collect a rangom sample of 64 credit cards issued during the
past 6 months. The sample meañ FICO ščóre of the credit' čārd 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 =
%D
76, the standard deviation from
the NBER study.
Let u equal the true population mean,FICO score for consumers issued credit cards in the past 6
months. Yöu should formulate the nüll' and ălternative hypotheses as:
O Ho: x =
731, H1: x < 731
Ho: µ =
731, Η 1: μ < 731
O Ho: H < 731, H1: µ = 731
Họ: µ =
731, Η1: μ > 731
If the null hypothesis is true as an equality, the sampling distribution of x is approximated by
a normal
distribution with
a mean of 731
and a standard deviation of
9.5
The value of the standardized test statistic is z = -1.47
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%2F4e5359bc-2f7f-4493-86fb-404323db7989%2Forxtf54_processed.png&w=3840&q=75)
Transcribed Image Text:mean FICO Score for the credit card holder (at the time the card waş issued),9ávið Láibson,
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 FICO
Score is perceived to be a low crediť risk to thě léňdeř andď is more likely to be extended' credit than
a consurmēr with a TOw Score.
A credit, card represents, a line of credit,,bęcause 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
731 and a standard
deviation of (6. TSource: Sumit Agarwar, John C. DriscoL Xayier Gapaix, and
Learning in the Credit Card Market,"Wörking Paper 13822, Nätional Büřeau of Economic Research
(NBER), Fébrüary 2008.]
You .conduct a hypothesis
ISsuing credit cards since 26028Atermune whether banks have loosened their standards for
You collect a rangom sample of 64 credit cards issued during the
past 6 months. The sample meañ FICO ščóre of the credit' čārd 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 =
%D
76, the standard deviation from
the NBER study.
Let u equal the true population mean,FICO score for consumers issued credit cards in the past 6
months. Yöu should formulate the nüll' and ălternative hypotheses as:
O Ho: x =
731, H1: x < 731
Ho: µ =
731, Η 1: μ < 731
O Ho: H < 731, H1: µ = 731
Họ: µ =
731, Η1: μ > 731
If the null hypothesis is true as an equality, the sampling distribution of x is approximated by
a normal
distribution with
a mean of 731
and a standard deviation of
9.5
The value of the standardized test statistic is z = -1.47
Use the Distributions tool to help you answer the questions that follow.
Transcribed Image Text:Normal Distribution
Mean = 730
Standard Deviation
8.5
%3D
710
720
730
740
75(X
-2
-1
1
2
You conduct the hypothesis teşt using a şignificance level of a = 0.10. Use the tool to develop the
rejection region föf your test. According tớ thế critičal vālue approäch, when do you reječt the nüll
hypothesis?
Reject H1 if z< -1.282
Reject Ho if z < -1.645 or z > 1.645
o Reject H, if z < -1.282
Reject H, if z > -1.47
The p-value is 0.0708
Using the critical value approach, the null hypothesis is
-1.47 < -1.282 ▼ . Using the p-value approach, the null hypothesis is
because 0.0708 < 0.10
their standards for issuing credit cards since 2002.
rejected
because
rejected
conclude that banks have loosened
Therefore, you
can
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