Please help with the question below Also please scroll over

Please help with the question below. Also, please scroll over. I could not copy the entire question on the page

2. Hypothesis tests about a population mean, population standard deviation known Aa Aa 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 mearn FICO score of the credit card holders (at the time their cards were issued) is -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 = 76 the standard deviation from the NBER study You conduct the hypothesis test using a significance level of = .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? O Reject Ho if z s -1.96 or z 2 1.96 O Reject Ho if z 2 -1.18 O Reject Ha if z s -1.645 O Reject Ho if z s -1.645 Let 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: Ho: 731, Hai 731 Ho:2731, Hai

Solution

Set Up Hypothesis
Null Hypothesis H0: U>=731
Alternate Hypothesis H1: U<731
Test Statistic
Population Mean(U)=731
Given That X(Mean)=722
Standard Deviation(S.D)=76
Number (n)=100
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=722-731/(76/Sqrt(100)
Zo =-1.1842
| Zo | =1.1842
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =1.1842 & | Z | =1.645
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Left Tail - Ha : ( P < -1.1842 ) = 0.1182
Hence Value of P0.05 < 0.1182, Here We Do not Reject Ho

[ASNWERS]
1.Ho: u>=731, H1<731
2. nomally distribution, 76
3. Test statistic: Zo =-1.1842
4. Reject Ho, if Z0<= -1.645
5. ( P < -1.1842 ) = 0.1182