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 708.8. 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 45 high - income individuals and found the sample mean credit score to be 727.5 with a standard deviation of 83.9. conduct the appropriate test to determine if high - income individuals have higher credit scores at the α = 0.05 level of significance.
state the null and alternative hypotheses.
h₀: μ = 708.8
h₁: μ > 708.8
(type integers or decimals. do not round.)
identify the t - statistic.
t₀ = 1.50 (round to two decimal places as needed.)
identify the p - value.
p - value = (round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 45\). So \(df=45-1 = 44\)

Step2: Use the t - distribution table or calculator

We have a one - tailed t - test (since \(H_1:\mu>708.8\)) with \(t_0 = 1.50\) and \(df = 44\). Using a t - distribution calculator or software (for example, in R: pt(1.50,44,lower.tail = FALSE) or in Excel: =T.DIST.RT(1.50,44)), we find the P - value.

Answer:

\(P-\text{value}\approx0.072\)