In: Statistics and Probability
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.
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.