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 700.5. 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 42 ​high-income individuals and found the sample mean credit score to be 718.3 with a standard deviation of 81.2. 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 equals greater than not equals nothing Upper H 1​: mu ▼ not equals less than equals greater than 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 not is sufficient evidence to claim that the mean credit score of​ high-income individuals is ▼ less than greater than equal to nothing. Enter your answer in each of the answer boxes.

Answer 1

Here using ti-83 calculator.

Test Hypothesis :-

Test statistic :-

t = 1.42

P-value :-

P=0.081

Conclusion :-

Fail to reject the null hypothesis. There is not sufficient evidence to claim that the mean credit score of high-income individual is greater than 700.5