Question

A credit score is used by credit agencies​ (such as mortgage companies and​ banks) to assess the creditworthiness of individuals. Values range from 300 to​ 850, with a credit score over 700 considered to be a quality credit risk. According to a​ survey, the mean credit score is 705.9. A credit analyst wondered whether​ high-income individuals​ (incomes in excess of​ $100,000 per​ year) had higher credit scores. He obtained a random sample of 39 ​high-income individuals and found the sample mean credit score to be 718.1 with a standard deviation of 81.7. Conduct the appropriate test to determine if​ high-income individuals have higher credit scores at the alphaequals0.05 level of significance. State the null and alternative hypotheses. Upper H 0​: mu ▼ less than not equals equals greater than nothing Upper H 1​: mu ▼ not equals less than greater than equals nothing ​(Type integers or decimals. Do not​ round.) Identify the​ t-statistic. t 0equals nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) Make a conclusion regarding the hypothesis. ▼ Reject Fail to reject the null hypothesis. There ▼ is is not sufficient evidence to claim that the mean credit score of​ high-income individuals is ▼ less than equal to greater than nothing.

Answer 1

1. Null and Alternative Hypothesis:

H0: High income individuals have not higher credit scores

H1: High income individuals have higher credit scores

i.e.

i.e. thus we conclude that High income individuals have not higher credit scores