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 704.2. 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 34 high-income individuals and found the sample mean credit score to be 715.3 with a standard deviation of 82.5. Conduct the appropriate test to determine if high-income individuals have higher credit scores at the a= 0.05 level of significance. TEL State the null and alternative hypotheses. Ho: H = 704.2 P H₁> 7,04.2 (Type integer or decimals. Do not round.) Identify the t-statistic. to = (Round to two decimal places as needed.)
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 704.2. 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 34 high-income individuals and found the sample mean credit score to be 715.3 with a standard deviation of 82.5. Conduct the appropriate test to determine if high-income individuals have higher credit scores at the a= 0.05 level of significance. TEL State the null and alternative hypotheses. Ho: H = 704.2 P H₁> 7,04.2 (Type integer or decimals. Do not round.) Identify the t-statistic. to = (Round to two decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Understanding Credit Scores and Hypothesis Testing
#### Overview
A credit score is utilized by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. These scores range from 300 to 850, with a score over 700 considered to be a quality credit risk. According to a survey, the mean credit score is 704.2.
A credit analyst questioned whether high-income individuals (incomes exceeding $100,000 per year) tend to have higher credit scores. To investigate this, a random sample of 34 high-income individuals was taken, finding a sample mean credit score of 715.3 with a standard deviation of 82.5. The task is to conduct a hypothesis test at the \(\alpha = 0.05\) level of significance to determine if high-income individuals have significantly higher credit scores.
#### Hypotheses
- **Null Hypothesis (\(H_0\))**: \(\mu = 704.2\)
- **Alternative Hypothesis (\(H_1\))**: \(\mu > 704.2\)
#### Calculating the T-statistic
To test the hypotheses, the analyst must identify the t-statistic. The formula to calculate the t-statistic in this context is not provided in the image, but typically, it is calculated as follows:
\[
t = \frac{\bar{x} - \mu}{s/\sqrt{n}}
\]
where:
- \(\bar{x}\) = sample mean (715.3)
- \(\mu\) = population mean (704.2)
- \(s\) = sample standard deviation (82.5)
- \(n\) = sample size (34)
The t-statistic should be rounded to two decimal places as needed. After computing the value, it can be compared against the critical t-value from the t-distribution table for \(n-1\) degrees of freedom at the \(\alpha = 0.05\) significance level to draw conclusions from the hypothesis test.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e5d1fcc-dc4e-459d-accd-b833757f73de%2F3422e36e-bf5f-4957-9ece-7c963f6176b6%2Fljc8zc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Credit Scores and Hypothesis Testing
#### Overview
A credit score is utilized by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. These scores range from 300 to 850, with a score over 700 considered to be a quality credit risk. According to a survey, the mean credit score is 704.2.
A credit analyst questioned whether high-income individuals (incomes exceeding $100,000 per year) tend to have higher credit scores. To investigate this, a random sample of 34 high-income individuals was taken, finding a sample mean credit score of 715.3 with a standard deviation of 82.5. The task is to conduct a hypothesis test at the \(\alpha = 0.05\) level of significance to determine if high-income individuals have significantly higher credit scores.
#### Hypotheses
- **Null Hypothesis (\(H_0\))**: \(\mu = 704.2\)
- **Alternative Hypothesis (\(H_1\))**: \(\mu > 704.2\)
#### Calculating the T-statistic
To test the hypotheses, the analyst must identify the t-statistic. The formula to calculate the t-statistic in this context is not provided in the image, but typically, it is calculated as follows:
\[
t = \frac{\bar{x} - \mu}{s/\sqrt{n}}
\]
where:
- \(\bar{x}\) = sample mean (715.3)
- \(\mu\) = population mean (704.2)
- \(s\) = sample standard deviation (82.5)
- \(n\) = sample size (34)
The t-statistic should be rounded to two decimal places as needed. After computing the value, it can be compared against the critical t-value from the t-distribution table for \(n-1\) degrees of freedom at the \(\alpha = 0.05\) significance level to draw conclusions from the hypothesis test.
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