A credit score is used by credit agencies such as mortgage companies and banks to assess the creditworthiness of individuals values range from 300-850with a credit score over 700 considered to be a quality credit risk according to a survey the mean credit score is 708.8 a credit analyst wondered whether high income individuals income excess of 100,000 per year had higher credit score he obtained a random sample of 45 high incomes individuals and found the sample mean credit score to be 720.5 with standard deviation of 83.9 conduct the appropriate test to determine if high income individuals have higher credit scores at a=0.05 level of significance
The appropriate test to determine if high income individuals have higher credit scores at a=0.05 level of significance is a two-tailed t-test. The null hypothesis is that there is no difference between the mean credit score of high income individuals and the population mean credit score of 708.8. The alternative hypothesis is that high income individuals have a higher mean credit score than the population mean. The t-test statistic is calculated as (720.5-708.8)/(83.9/√45) = 2.14. The critical value for a two-tailed t-test at a=0.05 is 2.01. Since the t-test statistic is greater than the critical value, we can reject the null hypothesis and conclude that high income individuals have a higher mean credit score than the population mean.
