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 703.2. 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 44 high-income individuals and found the sample mean credit score to be 714.7 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. Hoiul Hyp (Type integers or decimals. Do not round.) Identify the t-statistic to-(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 greater than equal to less than

Answer 1

Given,

$\small \mu= 714.7$

$\small \sigma= 82.9$

$\small n = 44$

The hypothesis is,

$\small H_0 : \mu = 703.2$

$\small H_0 : \mu > 703.2$

The test statistic is,

$\small t = \frac{\mu-703.2}{\frac{s}{\sqrt n}}$

$\small t = \frac{714.7-703.2}{\frac{82.9}{\sqrt 44}}$

$\small t = 0.92$

The P-value is,

$\small P-value = 0.181$

The conclusion is,

Fail to reject null hypothesis. There is not sufficient evidence to claim that the mean credit score of high-income individual is greater than 703.2

2.

The difference between an independent and dependent sample is,

D. A sample is independent when an individual selected for one sample does not dictate which individual is to be in the second sample. A sample is dependent when an individual selected for one sample dictate which individual is to be in the second sample.

3.

The 12th percentile is,

The z score corresponding to 12 th percentile is -1.175

we know that,

$\small z=\frac{x-\mu}{\sigma}$

$\small -1.175=\frac{x-54}{7}$

$\small x = 45.775$