Question

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 mean FICO score of the credit card holders (at the time their cards were issued) is X = 717. Assume that the standard pulation of FIC the standard deviation from the NBER study scores for credit cards issued during the past 6 months is known to be o: deviation of the 76, Let u 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: O Ho: H 2 731, Ha: u < 731 Ho: H 731, Ha: u > 731 O Ho: x z 731, Ha: X < 731 O Ho: H731, Ha: u 2 731 If the null hypothesis is true as an equality, the sampling distribution of X is approximated by distribution with and a standard deviation of The value of the standardized test statistic is Session

Answer 1

A hypothesis formulated helps to test whether banks have loosened their standards for issuing credit cards.If the credit card score in the last 6 months is less than avg, credit score initially,the standards have loosened as the banks have issued credit cards to low scorers.

1.Our hypothesis is

Ho u<731

Ha =u>731

Ho
tests if the the avg. credit score has fallen below 731.If
Ho
is rejected,we can conclude that the avg credit score for issuing credit cards have risen. i.e. standards have tightened.. If
Ho
is not rejected, standards have loosened.(Avg. credit card scores have fallen.)

We have used $\mu$ and not $\overline{x}$ because our aim is to test for the avg. credit score of the population and not of a sample of the population.In conclusion, option b. is correct.

2.If the null hypothesis is true as an inequality, the sampling distribution of $\overline{x}$ is formulated as a Normal distribution because population s.d.(
g=0.76
) is known. When population s.d. is not known,$\overline{x}$ follows t-dist.

If the null hypothesis is true as a an equality, the sampling distribution of $\overline{x}$ is approximated by a standard normal distribution with mean 731 and standard deviation=
76 V100 /n
.

[Since ].i.e. expectation of sample mean equals population mean.

E=

3.The value of standardized test statistic is
T E(T) s.e. ( Vn

717 731 -1.842 76 100

4.For a left,one- tailed hypothesis ,a standard normal distribution at 10 % level of significance,the z-value(critical value) from the table is -1.282. Therefore,our null hypothesis is rejected,if computed z-statistic is less than the tabulated z-statistic(critical value). option a. is correct. Reject H0 if  .

1.282

ue Acce prance Region 842-1.28 2 Ctabulated walua CS Scanned with CamScanner

5.p-value corresponding to 1.842 is .0327. (look up the probability of 1.842 from std. normal distribution tables and subtract 1 from it)

6.Using the critical value approach,the Null hypothesis is rejected because critical value(-1.282) higher than computed value(-1.842).Using the p-value approach,the null hypothesis is rejected, because p value(0.0327) is less than level of significance (0.10). Therefore ,you cannot conclude that banks have loosened their standards for issuing credit cards since 2002.