e work she a = .01, test the claim that p> 0, there is a correlation between list price and invoice price.

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**Correlation Analysis for Educational Purposes**

This discussion involves an analysis of the correlation between list price and invoice price. The data collection and analysis techniques used here can be applied across various educational settings to demonstrate statistical concepts.

**Objective:**

To understand the relationship between list price and invoice price by testing the claim that the correlation coefficient \( \rho \) (rho) is greater than 0.

**Hypothesis Testing:**

- **Null Hypothesis (\(H_0\))**: \( \rho \leq 0 \)
- **Alternative Hypothesis (\(H_A\))**: \( \rho > 0 \)

**Significance Level:**

For this test, we will use a significance level (\( \alpha \)) of 0.01.

**Procedure:**

1. **Data Collection:** Collect a sample of data that includes both list prices and invoice prices.
2. **Calculate Correlation Coefficient:** Compute the correlation coefficient for the sample data.
3. **Test the Hypothesis:** Use statistical methods (e.g., t-test for correlation) to test the hypothesis at \( \alpha = 0.01 \).

**Expected Outcomes and Analysis:**

- If the test statistic falls within the critical region, reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that there is a positive correlation between list price and invoice price.
- If the test statistic does not fall within the critical region, fail to reject the null hypothesis. This suggests that there is not sufficient evidence to support the claim, and the correlation is not significantly greater than zero.

By conducting such a hypothesis test, students can learn about the significance of correlations in data analysis and how to statistically test relationships between variables.
Transcribed Image Text:**Correlation Analysis for Educational Purposes** This discussion involves an analysis of the correlation between list price and invoice price. The data collection and analysis techniques used here can be applied across various educational settings to demonstrate statistical concepts. **Objective:** To understand the relationship between list price and invoice price by testing the claim that the correlation coefficient \( \rho \) (rho) is greater than 0. **Hypothesis Testing:** - **Null Hypothesis (\(H_0\))**: \( \rho \leq 0 \) - **Alternative Hypothesis (\(H_A\))**: \( \rho > 0 \) **Significance Level:** For this test, we will use a significance level (\( \alpha \)) of 0.01. **Procedure:** 1. **Data Collection:** Collect a sample of data that includes both list prices and invoice prices. 2. **Calculate Correlation Coefficient:** Compute the correlation coefficient for the sample data. 3. **Test the Hypothesis:** Use statistical methods (e.g., t-test for correlation) to test the hypothesis at \( \alpha = 0.01 \). **Expected Outcomes and Analysis:** - If the test statistic falls within the critical region, reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that there is a positive correlation between list price and invoice price. - If the test statistic does not fall within the critical region, fail to reject the null hypothesis. This suggests that there is not sufficient evidence to support the claim, and the correlation is not significantly greater than zero. By conducting such a hypothesis test, students can learn about the significance of correlations in data analysis and how to statistically test relationships between variables.
### Dealer Invoice and List Price for Cars (in thousands of dollars)

This table shows the invoice price and the list price of cars in thousands of dollars. The data can be used to analyze the relationship between the invoiced price the dealer pays for the vehicle and the list price suggested for sale. The critical data points provided in this table are labeled as "x" for List Price and "y" for Invoice Price.

| Invoice Price (y) | List Price (x) |
|-------------------|----------------|
| 29.8              | 32.1           |
| 31.1              | 33.5           |
| 32.0              | 36.1           |
| 42.1              | 44.0           |
| 42.2              | 47.8           |

This table may offer insights into how much markup a dealer might apply to the invoice price to determine the final list price that consumers will see. The values are presented straightforwardly to enable easy comparison and analysis.

#### Analysis Guidelines
1. **Identify Trends**: Notice if there is a consistent pattern in how the list price increases relative to the invoice price.
2. **Calculate Markup**: For deeper analysis, calculate the percentage markup from the invoice price to the list price.
3. **Compare Market Models**: Such data can help in understanding how pricing strategies might differ across various car brands or models.

This data can be particularly useful for students studying economics, business, or anyone interested in understanding the automotive retail pricing strategies.
Transcribed Image Text:### Dealer Invoice and List Price for Cars (in thousands of dollars) This table shows the invoice price and the list price of cars in thousands of dollars. The data can be used to analyze the relationship between the invoiced price the dealer pays for the vehicle and the list price suggested for sale. The critical data points provided in this table are labeled as "x" for List Price and "y" for Invoice Price. | Invoice Price (y) | List Price (x) | |-------------------|----------------| | 29.8 | 32.1 | | 31.1 | 33.5 | | 32.0 | 36.1 | | 42.1 | 44.0 | | 42.2 | 47.8 | This table may offer insights into how much markup a dealer might apply to the invoice price to determine the final list price that consumers will see. The values are presented straightforwardly to enable easy comparison and analysis. #### Analysis Guidelines 1. **Identify Trends**: Notice if there is a consistent pattern in how the list price increases relative to the invoice price. 2. **Calculate Markup**: For deeper analysis, calculate the percentage markup from the invoice price to the list price. 3. **Compare Market Models**: Such data can help in understanding how pricing strategies might differ across various car brands or models. This data can be particularly useful for students studying economics, business, or anyone interested in understanding the automotive retail pricing strategies.
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