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 708.8. 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 45 high - income individuals and found the sample mean credit score to be 727.5 with a standard deviation of 83.9. conduct the appropriate test to determine if high - income individuals have higher credit scores at the \\( \alpha=0.05 \\) level of significance.

state the null and alternative hypotheses.

\\( h_{0}: \mu=708.8 \\)
\\( h_{1}: \mu>708.8 \\)
(type integers or decimals. do not round)

identify the t - statistic.

\\( t_{0}=1.50 \\) (round to two decimal places as needed.)

identify the p - value.

p - value \\( =0.072 \\) (round to three decimal places as needed.)

make a conclusion regarding the hypothesis.

the null hypothesis. there sufficient evidence to claim that the mean credit score of high - income individuals is

Explanation:

Step1: Compare P - value and significance level

We are given a significance level \(\alpha = 0.05\) and a P - value \(P=0.072\).

Step2: Make a decision

Since \(P = 0.072>0.05=\alpha\), we fail to reject the null hypothesis.

Answer:

Fail to reject the null hypothesis. There is not sufficient evidence to claim that the mean credit score of high - income individuals is greater than \(708.8\).