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 708.2. 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 34 ​high-income individuals and found the sample mean credit score to be 724.7 with a standard deviation of 80.3. Conduct the appropriate test to determine if​ high-income individuals have higher credit scores at the a=0.05 level of significance.

State the null and alternative hypotheses.

H0​: μ ______ _______

H1​: μ ______ _______

​(Type integers or decimals. Do not​ round.)

Answer 1

(a)

Question asked:

State the null and alternative hypotheses.

H0: (High - income individuals have credit scores of 708.2)

H1: (High - income individuals have higher credit scores)

(b)

SE = s/

= 80.3/

= 13.7713

Test Statistic is given by:

t = (724.7 - 708.2)/13.7713

= 1.1981

= 0.05

ndf = n - 1 = 34 - 1 = 33

One Tail - Right Side Test

From Table, critical value of t = 1.6924

Since calculated value of t = 1.1981 is less than critical value of t = 1.6924, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that high-income individuals have higher credit scores at the =0.05 level of significance.