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4. A marketing executive asks people in three different cities to name their favorite sport. Here are the results, organized in a table: 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 Can she say that the favorite sport may depend where people live? Type of Test: Null Hypothesis: Alternate Hypothesis:

4. A marketing executive asks people in three different cities to name their favorite sport. Here are the results, organized in a table: 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 Can she say that the favorite sport may depend where people live? Type of Test: Null Hypothesis: Alternate Hypothesis:

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### Analysis of Favorite Sports across Different Cities #### Research Scenario A marketing executive is investigating if the favorite sport of individuals varies across three different cities. The data was collected and organized into the following table: | 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 | #### Research Question Can the marketing executive conclude that the favorite sport is dependent on the city in which people live? #### Statistical Analysis 1. **Type of Test:** - Chi-Square Test of Independence 2. **Hypotheses:** - **Null Hypothesis (H₀):** The favorite sport is independent of the city where people live. (There is no association between the city and the choice of favorite sport.) - **Alternate Hypothesis (H₁):** The favorite sport depends on the city where people live. (There is an association between the city and the choice of favorite sport.) 3. **Test Statistic:** - Chi-Square (χ²) Statistic (To be calculated based on observed and expected frequencies) 4. **P-value:** - P-value (To be determined from the chi-square distribution table based on the test statistic and degrees of freedom) 5. **Decision:** - Compare the p-value with a significance level (commonly α = 0.05): - If p-value ≤ α, reject the null hypothesis. - If p-value > α, fail to reject the null hypothesis. 6. **Conclusion:** - Based on the decision rule, interpret whether there is enough evidence to suggest that the favorite sport is dependent on the city. ### Data Visualization The table provides categorical data about the number of individuals in three cities who chose a particular sport as their favorite. #### Sample Calculation (Example for Chi-Square Test) To calculate the chi-square statistic: 1. Calculate the expected frequency for each cell in the table. This involves using the formula: \[ E_{ij} = \frac{(row_i \ total) \times (column
Transcribed Image Text:### Analysis of Favorite Sports across Different Cities #### Research Scenario A marketing executive is investigating if the favorite sport of individuals varies across three different cities. The data was collected and organized into the following table: | 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 | #### Research Question Can the marketing executive conclude that the favorite sport is dependent on the city in which people live? #### Statistical Analysis 1. **Type of Test:** - Chi-Square Test of Independence 2. **Hypotheses:** - **Null Hypothesis (H₀):** The favorite sport is independent of the city where people live. (There is no association between the city and the choice of favorite sport.) - **Alternate Hypothesis (H₁):** The favorite sport depends on the city where people live. (There is an association between the city and the choice of favorite sport.) 3. **Test Statistic:** - Chi-Square (χ²) Statistic (To be calculated based on observed and expected frequencies) 4. **P-value:** - P-value (To be determined from the chi-square distribution table based on the test statistic and degrees of freedom) 5. **Decision:** - Compare the p-value with a significance level (commonly α = 0.05): - If p-value ≤ α, reject the null hypothesis. - If p-value > α, fail to reject the null hypothesis. 6. **Conclusion:** - Based on the decision rule, interpret whether there is enough evidence to suggest that the favorite sport is dependent on the city. ### Data Visualization The table provides categorical data about the number of individuals in three cities who chose a particular sport as their favorite. #### Sample Calculation (Example for Chi-Square Test) To calculate the chi-square statistic: 1. Calculate the expected frequency for each cell in the table. This involves using the formula: \[ E_{ij} = \frac{(row_i \ total) \times (column
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