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 702.6. 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 717.3 with a standard deviation of 81.9. Conduct the appropriate test to determine if​ high-income individuals have higher credit scores at the alphaequals0.05 level of significance

State the null and alternative hypotheses. Upper H 0​: mu ▼ equals less than not equals greater than nothing Upper H 1​: mu ▼

Identify the t-statistic

Identify the P-value

Make a conclusion regarding the hypothesis.

Answer 1

Answer:

sample size = n = 31

sample mean = xbar =717.3

sample standard deviation is s=81.9

Null and Alternative Hypotheses :

H0 : μ = 702.6
HA : μ > 702.6

This is a right tailed test,

The test statistics,

t =( - )/ (s /n)

= ( 717.3 - 702.6) / ( 81.9 / 31 )

= 0.9993

P-value = 0.161

The p-value is p = 0.161> 0.05,

it is concluded that the null hypothesis is fail to rejected

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