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 703.8. 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 40 ​high-income individuals and found the sample mean credit score to be 723.1 with a standard deviation of 82.2. Conduct the appropriate test to determine if​ high-income individuals have higher credit scores at the α=0.05 level of significance.

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

703.8.

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

40

​high-income individuals and found the sample mean credit score to be

723.1

with a standard deviation of

82.2.

Conduct the appropriate test to determine if​ high-income individuals have higher credit scores at the

α=0.05

level of significance.

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