Ford Car Sales Assume you are working as a statistician for the automotive company Ford. Ford's three most popular cars are the Escape (SUV), the Focus (midsize sedan), and the Fusion (hybrid sedan). Your boss is putting together next year's production numbers and asks you to determine if any of the three models are selling better or worse than the other two. You have the sales numbers from one month of sales: the Escape sold 22,274, the Focus sold 21,385, and the Fusion sold 20,808.* Perform the necessary test to determine if sales are significantly different and report the conclusion(s) of interest to your boss.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Chapter11: Data Analysis And Probability
Section11.3: Using Data Displays
Problem 1E
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### Analysis of Sales Performance Across Three Models

**Question:**
Is the evidence strong enough from this one month to conclude that sales are significantly different between the three models?

**Options:**
- ⃝ Yes
- ⃝ No

**Explanation:**
The question aims to determine whether the observed sales data from a single month can lead to a statistically significant conclusion about the differences in sales performance across three different models. 

When analyzing sales data, it's important to consider several factors such as the sample size, variability in the data, and the duration over which data is collected. One month's data might not provide a comprehensive understanding due to potential short-term fluctuations.

Choose "Yes" if you believe the data provided is sufficient to confirm a significant difference in sales performance.
Choose "No" if you think a longer observation period or more data is needed for a valid conclusion.
Transcribed Image Text:### Analysis of Sales Performance Across Three Models **Question:** Is the evidence strong enough from this one month to conclude that sales are significantly different between the three models? **Options:** - ⃝ Yes - ⃝ No **Explanation:** The question aims to determine whether the observed sales data from a single month can lead to a statistically significant conclusion about the differences in sales performance across three different models. When analyzing sales data, it's important to consider several factors such as the sample size, variability in the data, and the duration over which data is collected. One month's data might not provide a comprehensive understanding due to potential short-term fluctuations. Choose "Yes" if you believe the data provided is sufficient to confirm a significant difference in sales performance. Choose "No" if you think a longer observation period or more data is needed for a valid conclusion.
### Ford Car Sales

Assume you are working as a statistician for the automotive company Ford. Ford's three most popular cars are the Escape (SUV), the Focus (midsize sedan), and the Fusion (hybrid sedan). Your boss is putting together next year’s production numbers and asks you to determine if any of the three models are selling better or worse than the other two. You have the sales numbers from one month of sales: the Escape sold 22,274, the Focus sold 21,385, and the Fusion sold 20,808. Perform the necessary test to determine if sales are significantly different and report the conclusion(s) of interest to your boss.

*Sales from **The Wall Street Journal** for June 2011.

---

### Calculate the chi-square test statistic and the p-value.

Round your answer for the chi-square statistic to the nearest integer, and your answer for the p-value to three decimal places.

- \( \chi^2 = \) [Input field for chi-square value]
- p-value = [Input field for p-value]

---

### Explanation

This exercise involves calculating the chi-square (\( \chi^2 \)) test statistic and the corresponding p-value to assess if there is a significant difference in the sales numbers of the three Ford models. 

1. **Chi-Square Test Statistic:**
   - This is a measure used in statistics to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.
 
2. **P-Value:**
   - The p-value helps determine the significance of the results. A p-value less than 0.05 typically indicates that the observed differences are statistically significant.

#### Steps to Perform the Test:
1. **State the Hypotheses:**
   - Null Hypothesis (H0): There is no significant difference in the sales numbers of the three models.
   - Alternative Hypothesis (H1): There is a significant difference in the sales numbers of the three models.

2. **Calculate the Test Statistic:**
   - Use the provided sales numbers to compute the chi-square statistic.

3. **Determine the P-Value:**
   - Use the chi-square distribution table to find the p-value corresponding to the calculated chi-square statistic.

4. **Conclusion:**
   - Compare the p-value to the significance level (usually 0.05). If the p-value is less than the significance level, reject the null
Transcribed Image Text:### Ford Car Sales Assume you are working as a statistician for the automotive company Ford. Ford's three most popular cars are the Escape (SUV), the Focus (midsize sedan), and the Fusion (hybrid sedan). Your boss is putting together next year’s production numbers and asks you to determine if any of the three models are selling better or worse than the other two. You have the sales numbers from one month of sales: the Escape sold 22,274, the Focus sold 21,385, and the Fusion sold 20,808. Perform the necessary test to determine if sales are significantly different and report the conclusion(s) of interest to your boss. *Sales from **The Wall Street Journal** for June 2011. --- ### Calculate the chi-square test statistic and the p-value. Round your answer for the chi-square statistic to the nearest integer, and your answer for the p-value to three decimal places. - \( \chi^2 = \) [Input field for chi-square value] - p-value = [Input field for p-value] --- ### Explanation This exercise involves calculating the chi-square (\( \chi^2 \)) test statistic and the corresponding p-value to assess if there is a significant difference in the sales numbers of the three Ford models. 1. **Chi-Square Test Statistic:** - This is a measure used in statistics to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. 2. **P-Value:** - The p-value helps determine the significance of the results. A p-value less than 0.05 typically indicates that the observed differences are statistically significant. #### Steps to Perform the Test: 1. **State the Hypotheses:** - Null Hypothesis (H0): There is no significant difference in the sales numbers of the three models. - Alternative Hypothesis (H1): There is a significant difference in the sales numbers of the three models. 2. **Calculate the Test Statistic:** - Use the provided sales numbers to compute the chi-square statistic. 3. **Determine the P-Value:** - Use the chi-square distribution table to find the p-value corresponding to the calculated chi-square statistic. 4. **Conclusion:** - Compare the p-value to the significance level (usually 0.05). If the p-value is less than the significance level, reject the null
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