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 700.8. 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 31 high-income individuals and found the sample mean credit score to be 717.5 with a standard deviation of 83.6. 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. Ho:H VO H: HVO (Type integers or decimals. Do not round.) Identify the t-statistic. nd to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) Make a conclusion regarding the hypothesis. the null hypothesis. There sufficient evidence to claim that the mean credit score of high-income individuals is

Answer 1

From the given data,

Here,

Null and Alternative Hypotheses :

H0 : μ = 700.8
HA : μ > 700.8

This is a right tailed test,

The test statistics,

t =( $\bar x$ - $\mu$ )/ (s /$\sqrt{}$n)

= ( 717.5 - 700.8) / ( 83.6 / $\sqrt{}$ 31 )

= 1.112

P-value = 0.1375

The p-value is p = 0.1375 > 0.05,

it is concluded that the null hypothesis is fail to rejected. There is no sufficent evidence to claim that the mean credit score of high-income individual.