4. A survey of 40 home prices in a metropolitan area has the following results. Price Less than $200,000 Equal to $200,000 More than $200,000 Number of homes 13 27 1. Test the hypothesis that the median price in the metropolitan is $200,000
4. A survey of 40 home prices in a metropolitan area has the following results. Price Less than $200,000 Equal to $200,000 More than $200,000 Number of homes 13 27 1. Test the hypothesis that the median price in the metropolitan is $200,000
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![The image contains educational content focusing on statistical analysis related to home prices and regression models.
### Survey of Home Prices:
A survey of 40 home prices in a metropolitan area shows the following results:
- **Number of homes priced less than $200,000**: 13
- **Number of homes priced equal to $200,000**: 1
- **Number of homes priced more than $200,000**: 27
### Hypothesis Testing:
1. **Test if the median price in the metropolitan area is $200,000.**
2. **Test if the median price in the metropolitan area is more than $200,000.**
- **Significance level (α)**: 0.05 for both cases.
- Instructions include hypothesis formulation, use of the binomial approach, and detailed explanation of calculations with p-values included.
### Regression Analysis:
It is proposed that the annual return of a security and the market return are related by the following regression model:
\[ y = mx + b + \varepsilon \]
- **y**: Annual return of the security.
- **x**: Annual return of the market.
- **b**: Intercept.
- **ε**: Normally distributed noise.
#### Return Calculation:
\[ \text{Return} = \frac{\text{Value at end of year} + \text{received dividends during year} - \text{value at beginning of year}}{\text{value at beginning of year}} \]
### Instructions for Model Testing:
- Retrieve annual data on a security of choice.
- Choose a financial index (e.g., S&P 500) as the market indicator.
- Use data spanning 20 years.
- Perform regression analysis to test the hypothesis.
- Include results and conclusions, significances, final regression model, coefficient of determination, and graphs (regression line, scatterplot, residuals).
Questions to Address:
- Model validity assessment.
- Positive or adverse influence determination.
- Explanation of results in terms of market performance.
This educational content directs students or users through practical statistical tasks, encouraging application and evaluation of statistical tests and models.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc75a416e-7821-4c4b-a434-6da28bc582d4%2F139d26dd-9d72-446c-8dce-424fb9cad27d%2Fslra02_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains educational content focusing on statistical analysis related to home prices and regression models.
### Survey of Home Prices:
A survey of 40 home prices in a metropolitan area shows the following results:
- **Number of homes priced less than $200,000**: 13
- **Number of homes priced equal to $200,000**: 1
- **Number of homes priced more than $200,000**: 27
### Hypothesis Testing:
1. **Test if the median price in the metropolitan area is $200,000.**
2. **Test if the median price in the metropolitan area is more than $200,000.**
- **Significance level (α)**: 0.05 for both cases.
- Instructions include hypothesis formulation, use of the binomial approach, and detailed explanation of calculations with p-values included.
### Regression Analysis:
It is proposed that the annual return of a security and the market return are related by the following regression model:
\[ y = mx + b + \varepsilon \]
- **y**: Annual return of the security.
- **x**: Annual return of the market.
- **b**: Intercept.
- **ε**: Normally distributed noise.
#### Return Calculation:
\[ \text{Return} = \frac{\text{Value at end of year} + \text{received dividends during year} - \text{value at beginning of year}}{\text{value at beginning of year}} \]
### Instructions for Model Testing:
- Retrieve annual data on a security of choice.
- Choose a financial index (e.g., S&P 500) as the market indicator.
- Use data spanning 20 years.
- Perform regression analysis to test the hypothesis.
- Include results and conclusions, significances, final regression model, coefficient of determination, and graphs (regression line, scatterplot, residuals).
Questions to Address:
- Model validity assessment.
- Positive or adverse influence determination.
- Explanation of results in terms of market performance.
This educational content directs students or users through practical statistical tasks, encouraging application and evaluation of statistical tests and models.
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