Bradley Mullins
02/20/2024 · Middle School

\( 16 \begin{array}{l}\text { A credit score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. } \\ \text { Values range from } 300 \text { to } 850, \text { with a credit score over } 700 \text { considered to be a quality credit risk. According to a survey, the mean credit } \\ \text { score is } 706.1 \text {. A credit analyst wondered whether high-income individuals (incomes in excess of } \$ 100,000 \text { per year) had higher credit } \\ \text { scores. He obtained a random sample of } 45 \text { high-income individuals and found the sample mean credit score to be } 719.6 \text { with a } \\ \text { standard deviation of } 84.2 \text {. Conduct the appropriate test to determine if high-income individuals have higher credit scores at the } \\ \alpha=0.05 \text { level of significance. } \\ \text { Click the icon to view the table of critical } t \text {-values. }\end{array} \)

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Conduct a one-sample t-test with a calculated t-statistic of approximately 1.075 and a critical t-value of approximately 1.679. Fail to reject the null hypothesis at the \(\alpha = 0.05\) level, concluding there is not enough evidence to suggest high-income individuals have higher credit scores.

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