A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![**Regression Analysis of Used Car Prices**
In order to examine the relationship between the selling price of a used car and its age, an analyst uses data from 20 recent transactions and estimates the equation:
\[ \text{Price} = \beta_0 + \beta_1 \text{Age} + \varepsilon \]
A portion of the regression results is shown in the accompanying table.
| | Coefficients | Standard Error | t Stat | p-value |
|----------------|--------------|----------------|--------|-----------|
| Intercept | 21,268.91 | 732.41 | 29.040 | 1.42E-16 |
| Age | -1,201.23 | 128.98 | - | 2.64E-08 |
1. **Hypotheses Specification:**
Specify the competing hypotheses to determine whether the selling price of a used car and its age are linearly related.
- \( H_0: \beta_1 \ge 0; \) \( H_A: \beta_1 < 0 \)
- \( H_0: \beta_1 = 0; \) \( H_A: \beta_1 \neq 0 \)
- \( H_0: \beta_1 \le 0; \) \( H_A: \beta_1 > 0 \)
2. **Calculate the Test Statistic:**
Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
- Test statistic box for input.
3. **Find the p-value:**
- \( \text{p-value} \ge 0.10 \)
- \( 0.05 \le \text{p-value} < 0.10 \)
- \( 0.02 \le \text{p-value} < 0.05 \)
- \( 0.01 \le \text{p-value} < 0.02 \)
- \( \text{p-value} < 0.01 \)
4. **Significance at the 5% Level:**
At the 5% significance level, is the age of a used car significant in explaining its selling price?
- Conclusion box for input: " , we conclude that the](https://content.bartleby.com/qna-images/question/80f5a0b5-fa3f-4609-a3a3-be6affb5f07a/5dc7853e-dcfd-4616-8dc5-a375b18a343c/bzl8td_processed.png)
Transcribed Image Text:**Regression Analysis of Used Car Prices**
In order to examine the relationship between the selling price of a used car and its age, an analyst uses data from 20 recent transactions and estimates the equation:
\[ \text{Price} = \beta_0 + \beta_1 \text{Age} + \varepsilon \]
A portion of the regression results is shown in the accompanying table.
| | Coefficients | Standard Error | t Stat | p-value |
|----------------|--------------|----------------|--------|-----------|
| Intercept | 21,268.91 | 732.41 | 29.040 | 1.42E-16 |
| Age | -1,201.23 | 128.98 | - | 2.64E-08 |
1. **Hypotheses Specification:**
Specify the competing hypotheses to determine whether the selling price of a used car and its age are linearly related.
- \( H_0: \beta_1 \ge 0; \) \( H_A: \beta_1 < 0 \)
- \( H_0: \beta_1 = 0; \) \( H_A: \beta_1 \neq 0 \)
- \( H_0: \beta_1 \le 0; \) \( H_A: \beta_1 > 0 \)
2. **Calculate the Test Statistic:**
Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
- Test statistic box for input.
3. **Find the p-value:**
- \( \text{p-value} \ge 0.10 \)
- \( 0.05 \le \text{p-value} < 0.10 \)
- \( 0.02 \le \text{p-value} < 0.05 \)
- \( 0.01 \le \text{p-value} < 0.02 \)
- \( \text{p-value} < 0.01 \)
4. **Significance at the 5% Level:**
At the 5% significance level, is the age of a used car significant in explaining its selling price?
- Conclusion box for input: " , we conclude that the
![**d-1.** Conduct a hypothesis test at the 5% significance level in order to determine if \( a_1 \) differs from -1,000. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
**Test statistic:** [Text box]
**d-2.** Find the \( p \)-value.
- \( 0.05 \leq \) \( p \)-value \( < 0.10 \)
- \( 0.02 \leq \) \( p \)-value \( < 0.05 \)
- \( 0.01 \leq \) \( p \)-value \( < 0.02 \)
- \( p \)-value \( < 0.01 \)
- \( p \)-value \( \geq 0.10 \)
**d-3.** What is the conclusion to the test?
\[ H_0, \text{ we} \] [Dropdown] conclude that \(\beta_1 \neq -1,000 \)](https://content.bartleby.com/qna-images/question/80f5a0b5-fa3f-4609-a3a3-be6affb5f07a/5dc7853e-dcfd-4616-8dc5-a375b18a343c/w7334sx_processed.png)
Transcribed Image Text:**d-1.** Conduct a hypothesis test at the 5% significance level in order to determine if \( a_1 \) differs from -1,000. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
**Test statistic:** [Text box]
**d-2.** Find the \( p \)-value.
- \( 0.05 \leq \) \( p \)-value \( < 0.10 \)
- \( 0.02 \leq \) \( p \)-value \( < 0.05 \)
- \( 0.01 \leq \) \( p \)-value \( < 0.02 \)
- \( p \)-value \( < 0.01 \)
- \( p \)-value \( \geq 0.10 \)
**d-3.** What is the conclusion to the test?
\[ H_0, \text{ we} \] [Dropdown] conclude that \(\beta_1 \neq -1,000 \)
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