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 700.9. 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 41 ​high-income individuals and found the sample mean credit score to be 720.3 with a standard deviation of 83.1. Conduct the appropriate test to determine if​ high-income individuals have higher credit scores at the alpha equals 0.05 level of significance.

Answer 1

Given: = 700.9, = 720.3, s = 83.1, n = 41, = 0.05

The Hypothesis:

H0: = 700.9

Ha: > 700.9

This is a right tailed Test.

The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

The p Value:    The p value (Right Tail) for t = 1.49, for degrees of freedom (df) = n-1 = 40, is; p value = 0.072

The Critical Value:   The critical value (Right Tail) at = 0.05, for df = 40, tcritical = + 1.684

The Decision Rule:   If t observed is > t critical, then Reject H0

Also if P value is < , Then Reject H0.

The Decision:   Since t observed (1.49) is < t critical (1.684), We Fail to Reject H0.

Also since P value (0.072) is > (0.05) , We Fail to Reject H0.

The Conclusion: There isn't sufficient evidence at the 95% significance level to conclude that the high income individuals have higher credit scores.