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 701.2. 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 43 ​high-income individuals and found the sample mean credit score to be 715.8 with a standard deviation of 83.4.

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.

Upper H0: μ (<,=,≠,>) and _.

Upper H1: μ (<,=,≠,>) and _.

​(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.

("Fail to reject" or "reject") the null hypothesis. There (is, or is not) sufficient evidence to claim that the mean credit score of​ high-income individuals is

▼

(greater than, less than, equal to) _.

Answer 1

As the p value = 0.128 > 0.05 = level of significance, we do not reject Ho and conclude that the mean credit score for high income individuals is not significantly greater than 701.2