MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![### Statistical Analysis Problem
#### Instructions:
1. **Find the value of the test statistic.** (Round your answer to two decimal places.)
- **Test statistic value:** [Input box]
2. **Find the p-value.** (Round your answer to three decimal places.)
- **p-value:** [Input box]
3. **State your conclusion.**
- [ ] **Reject \( H_0 \):** We conclude that the relationship between weight (pounds) and price ($) is significant.
- [ ] **Reject \( H_0 \):** We cannot conclude that the relationship between weight (pounds) and price ($) is significant.
- [ ] **Do not reject \( H_0 \):** We conclude that the relationship between weight (pounds) and price ($) is significant.
- [ ] **Do not reject \( H_0 \):** We cannot conclude that the relationship between weight (pounds) and price ($) is significant.
#### Tips:
- Make sure to correctly calculate and round the test statistic to two decimal places.
- After finding the test statistic, use the appropriate statistical software or tables to determine the p-value, rounded to three decimal places.
- Based on the p-value and the chosen significance level (commonly \( \alpha = 0.05 \)), make your conclusion by selecting the appropriate option.
This problem helps you understand the process of hypothesis testing and the importance of correct rounding and interpretation of statistical results.](https://content.bartleby.com/qna-images/question/ac470ff6-15fd-4fdc-a5f2-c97f7b5a1d30/5de527a3-3ac0-4eb5-8ec4-bef4dda5c51d/zys7z_processed.jpeg)
Transcribed Image Text:### Statistical Analysis Problem
#### Instructions:
1. **Find the value of the test statistic.** (Round your answer to two decimal places.)
- **Test statistic value:** [Input box]
2. **Find the p-value.** (Round your answer to three decimal places.)
- **p-value:** [Input box]
3. **State your conclusion.**
- [ ] **Reject \( H_0 \):** We conclude that the relationship between weight (pounds) and price ($) is significant.
- [ ] **Reject \( H_0 \):** We cannot conclude that the relationship between weight (pounds) and price ($) is significant.
- [ ] **Do not reject \( H_0 \):** We conclude that the relationship between weight (pounds) and price ($) is significant.
- [ ] **Do not reject \( H_0 \):** We cannot conclude that the relationship between weight (pounds) and price ($) is significant.
#### Tips:
- Make sure to correctly calculate and round the test statistic to two decimal places.
- After finding the test statistic, use the appropriate statistical software or tables to determine the p-value, rounded to three decimal places.
- Based on the p-value and the chosen significance level (commonly \( \alpha = 0.05 \)), make your conclusion by selecting the appropriate option.
This problem helps you understand the process of hypothesis testing and the importance of correct rounding and interpretation of statistical results.
![### Analysis of Road-Racing Bikes Data
Below is the data for weight (in pounds) and price (in dollars) for 10 road-racing bikes.
| Brand | Weight (pounds) | Price ($) |
|-------|------------------|-----------|
| A | 17.8 | 2,100 |
| B | 16.1 | 6,350 |
| C | 14.9 | 8,370 |
| D | 15.9 | 6,200 |
| E | 17.2 | 4,000 |
| F | 13.1 | 8,700 |
| G | 16.2 | 6,000 |
| H | 17.1 | 2,680 |
| I | 17.6 | 3,500 |
| J | 14.1 | 8,000 |
The estimated regression equation based on the provided data is:
\[ \hat{y} = 28,621 - 1,439x \]
Where:
- \( \hat{y} \) is the predicted price.
- \( x \) is the weight of the bike.
For the given data, the values for Sum of Squared Errors (SSE) and Total Sum of Squares (SST) are:
- SSE = 6,824,137.81
- SST = 51,870,800
An F test will be used to determine whether the weight of a bike and its price are related at the 0.05 level of significance.
### Hypotheses
We will state the null and alternative hypotheses:
1. Null Hypothesis (\( H_0 \)): \( \beta_1 = 0 \)
2. Alternative Hypothesis (\( H_a \)): \( \beta_1 \neq 0 \)
### Determine the Test Statistic
To proceed with the analysis, calculate the value of the test statistic (t). Round your answer to two decimal places.
### Determine the p-value
Next, find the p-value (round your answer to three decimal places) to make a final conclusion about the relationship between bike weight and price.
By following these steps, we can analyze the data effectively to understand the significance of the relationship between the weight of road-racing bikes](https://content.bartleby.com/qna-images/question/ac470ff6-15fd-4fdc-a5f2-c97f7b5a1d30/5de527a3-3ac0-4eb5-8ec4-bef4dda5c51d/0s9wm2e_processed.jpeg)
Transcribed Image Text:### Analysis of Road-Racing Bikes Data
Below is the data for weight (in pounds) and price (in dollars) for 10 road-racing bikes.
| Brand | Weight (pounds) | Price ($) |
|-------|------------------|-----------|
| A | 17.8 | 2,100 |
| B | 16.1 | 6,350 |
| C | 14.9 | 8,370 |
| D | 15.9 | 6,200 |
| E | 17.2 | 4,000 |
| F | 13.1 | 8,700 |
| G | 16.2 | 6,000 |
| H | 17.1 | 2,680 |
| I | 17.6 | 3,500 |
| J | 14.1 | 8,000 |
The estimated regression equation based on the provided data is:
\[ \hat{y} = 28,621 - 1,439x \]
Where:
- \( \hat{y} \) is the predicted price.
- \( x \) is the weight of the bike.
For the given data, the values for Sum of Squared Errors (SSE) and Total Sum of Squares (SST) are:
- SSE = 6,824,137.81
- SST = 51,870,800
An F test will be used to determine whether the weight of a bike and its price are related at the 0.05 level of significance.
### Hypotheses
We will state the null and alternative hypotheses:
1. Null Hypothesis (\( H_0 \)): \( \beta_1 = 0 \)
2. Alternative Hypothesis (\( H_a \)): \( \beta_1 \neq 0 \)
### Determine the Test Statistic
To proceed with the analysis, calculate the value of the test statistic (t). Round your answer to two decimal places.
### Determine the p-value
Next, find the p-value (round your answer to three decimal places) to make a final conclusion about the relationship between bike weight and price.
By following these steps, we can analyze the data effectively to understand the significance of the relationship between the weight of road-racing bikes
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