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 709.7. 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 45 ​high-income individuals and found the sample mean credit score to be 722.4 with a standard deviation of 82.9. 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.)

Identify the​ t-statistic.

t0=______

​(Round 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

State the null and alternative hypotheses.

H0​: μ<=700

H1​: μ>700 ( this is right one-tailed test)

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

Identify the​ t-statistic.

t0=(x^--μ)/(s/sqrt(n))=(722.4-700)/(82.9/sqrt(45))=1.81 with n-1=45-1=44 df

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=0.039 ( using ms-excel==TDIST(1.81,44,1))

​(Round to three decimal places as​ needed.)

Make a conclusion regarding the hypothesis.

Reject the null hypothesis. There sufficient evidence to claim that the mean credit score of​ high-income individuals is have higher credit scores