Type of Test: Null Hypothesis: Alternate Hypothesi SE: Test Statistic: P-value: Decision: Sentence:

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### Analysis of Favorite Sports Across Three Cities

#### Introduction
A marketing executive conducted a survey asking people in three different cities to name their favorite sport. The data collected is organized in the following table:

#### Survey Data
| City         | Football | Baseball | Soccer | Basketball | Other |
|--------------|----------|----------|--------|------------|-------|
| Santa Barbara| 18       | 21       | 12     | 23         | 10    |
| Oxnard       | 24       | 11       | 28     | 15         | 14    |
| Los Angeles  | 22       | 25       | 15     | 34         | 11    |

The question to be analyzed is: **Can she say that the favorite sport may depend on where people live?**

#### Statistical Test Information

To answer this question, we will conduct a hypothesis test with the following details:

- **Type of Test:**
- **Null Hypothesis (H0):** There is no significant difference in the favorite sport distribution across the three cities. In other words, the favorite sport does not depend on the city.
- **Alternate Hypothesis (H1):** There is a significant difference in the favorite sport distribution across the three cities. In other words, the favorite sport depends on the city.
- **Standard Error (SE):**
- **Test Statistic:**
- **P-value:**
- **Decision:**
- **Conclusion Sentence:**

#### Explanation and Next Steps
To carry out this hypothesis test, one would typically use a chi-square test for independence because it is suitable for categorical data like favorite sports across different cities.

1. **Calculate the expected frequencies** for each cell in the table based on the overall distribution of favorite sports.
2. **Compute the chi-square test statistic** to measure how much the observed frequencies deviate from the expected frequencies.
3. **Determine the p-value**, which helps us decide whether to reject the null hypothesis.
4. **Make a decision** on whether the observed differences are statistically significant.

Based on the test results (which include the test statistic and p-value), the executive can conclude whether there is enough evidence to say that the favorite sport depends on the city.

Feel free to insert the specific values in the placeholders once the analysis is complete.
Transcribed Image Text:### Analysis of Favorite Sports Across Three Cities #### Introduction A marketing executive conducted a survey asking people in three different cities to name their favorite sport. The data collected is organized in the following table: #### Survey Data | City | Football | Baseball | Soccer | Basketball | Other | |--------------|----------|----------|--------|------------|-------| | Santa Barbara| 18 | 21 | 12 | 23 | 10 | | Oxnard | 24 | 11 | 28 | 15 | 14 | | Los Angeles | 22 | 25 | 15 | 34 | 11 | The question to be analyzed is: **Can she say that the favorite sport may depend on where people live?** #### Statistical Test Information To answer this question, we will conduct a hypothesis test with the following details: - **Type of Test:** - **Null Hypothesis (H0):** There is no significant difference in the favorite sport distribution across the three cities. In other words, the favorite sport does not depend on the city. - **Alternate Hypothesis (H1):** There is a significant difference in the favorite sport distribution across the three cities. In other words, the favorite sport depends on the city. - **Standard Error (SE):** - **Test Statistic:** - **P-value:** - **Decision:** - **Conclusion Sentence:** #### Explanation and Next Steps To carry out this hypothesis test, one would typically use a chi-square test for independence because it is suitable for categorical data like favorite sports across different cities. 1. **Calculate the expected frequencies** for each cell in the table based on the overall distribution of favorite sports. 2. **Compute the chi-square test statistic** to measure how much the observed frequencies deviate from the expected frequencies. 3. **Determine the p-value**, which helps us decide whether to reject the null hypothesis. 4. **Make a decision** on whether the observed differences are statistically significant. Based on the test results (which include the test statistic and p-value), the executive can conclude whether there is enough evidence to say that the favorite sport depends on the city. Feel free to insert the specific values in the placeholders once the analysis is complete.
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