Some travel agents claim that honeymoon hot spots vary according to the age of the bride. Suppose that 281 recent brides were interviewed as to where they spent their honeymoons. The information is given below. Conduct a test of independence at the 5% level. Location 20 - 29 30 - 39 40 - 49 50 and over Niagara Falls 15 26 24 20 Poconos 16 26 24 11 Europe 10 25 14 6 Virgin Islands 20 24 14 6

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### Educational Content: Statistical Analysis of Honeymoon Preferences by Age

Some travel agents claim that honeymoon hotspots vary according to the bride's age. A survey of 281 recent brides was conducted to find out where they spent their honeymoons. We are tasked with conducting a test of independence at the 5% significance level. Below is the data collected from the survey:

#### Data Table
| Location       | 20 - 29 | 30 - 39 | 40 - 49 | 50 and over |
|----------------|---------|---------|---------|-------------|
| Niagara Falls  | 15      | 26      | 34      | 20          |
| Poconos        | 16      | 26      | 24      | 11          |
| Europe         | 28      | 30      | 14      | 8           |
| Virgin Islands | 20      | 24      | 16      | 6           |

### Statistical Analysis Parts

#### Part (f)
**Question:** What is the p-value? (Round your answer to four decimal places.)

**Explanation:** Explain what the p-value means for this problem using the options provided:
1. If \( H_0 \) is false, there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
2. If \( H_0 \) is true, there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
3. If \( H_0 \) is true, there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
4. If \( H_0 \) is false, there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

#### Part (g)
**Task:** Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.

**Explanation of Graphs:**
- The graphs depict normal distribution curves.
- The x-axis is labeled as \( x^2 \) with the mean (\( \mu \)) marked.
- Each graph indicates shaded regions under the curve, representing the p-value.
  - In two graphs, the p-value region is on
Transcribed Image Text:### Educational Content: Statistical Analysis of Honeymoon Preferences by Age Some travel agents claim that honeymoon hotspots vary according to the bride's age. A survey of 281 recent brides was conducted to find out where they spent their honeymoons. We are tasked with conducting a test of independence at the 5% significance level. Below is the data collected from the survey: #### Data Table | Location | 20 - 29 | 30 - 39 | 40 - 49 | 50 and over | |----------------|---------|---------|---------|-------------| | Niagara Falls | 15 | 26 | 34 | 20 | | Poconos | 16 | 26 | 24 | 11 | | Europe | 28 | 30 | 14 | 8 | | Virgin Islands | 20 | 24 | 16 | 6 | ### Statistical Analysis Parts #### Part (f) **Question:** What is the p-value? (Round your answer to four decimal places.) **Explanation:** Explain what the p-value means for this problem using the options provided: 1. If \( H_0 \) is false, there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. 2. If \( H_0 \) is true, there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. 3. If \( H_0 \) is true, there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. 4. If \( H_0 \) is false, there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. #### Part (g) **Task:** Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. **Explanation of Graphs:** - The graphs depict normal distribution curves. - The x-axis is labeled as \( x^2 \) with the mean (\( \mu \)) marked. - Each graph indicates shaded regions under the curve, representing the p-value. - In two graphs, the p-value region is on
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