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 \\)
\\( h _ { 1 } : \mu \\)
(type
cimals. do not round.)

Explanation:

Step1: Determine the null hypothesis

The null hypothesis \(H_0\) is a statement of no - difference or no - effect. Here, we assume that there is no increase in the credit score of high - income individuals compared to the general population. So, \(H_0:\mu = 708.8\)

Step2: Determine the alternative hypothesis

The alternative hypothesis \(H_1\) is what we are trying to find evidence for. The credit analyst wants to know if high - income individuals have higher credit scores. So, \(H_1:\mu>708.8\)

Answer:

\(H_0:\mu = 708.8\)
\(H_1:\mu>708.8\)