A paired difference experiment yielded ng pairs of observations. In each case, what is the rejection region for testing Ho: Hd =2 against Ha: Hd > 2? a. ng = 11, a = 0.05 (Round to three decimal places as needed.) A V N v
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![### Paired Difference Experiment and Rejection Region
#### Problem Statement
A paired difference experiment yielded \( n_d \) pairs of observations. In each case, what is the rejection region for testing \(H_0: \mu_d = 2\) against \(H_a: \mu_d > 2\)?
#### Given Data
- \( n_d = 11 \)
- Significance level (\( \alpha \)) = 0.05
#### Task
Determine the t-value and specify the rejection region. Round the t-value to three decimal places as needed.
#### Solution Steps
1. **Compute the t-value:** Using the t-distribution table or computational tools, find the t-value for a one-tailed test with 10 degrees of freedom (since \( n_d - 1 = 11 - 1 = 10 \)) at \( \alpha = 0.05 \).
2. **Rejection Region:** After computing the t-value, determine the rejection region for the hypothesis test.
### Visual Elements
- **Dropdown Menus for Comparison Operators:** Choose the correct operator to fit the rejection region.
- `>`
- `<`
- `≥`
- `≤`
##### Instruction
- **Round to Three Decimal Places as Needed:** Ensure the precise calculation of the t-value and round it accordingly.
### Example Calculation
- Using the t-distribution table for a one-tailed test with \( df = 10 \) at \( \alpha = 0.05 \), the critical value \( t_{\alpha}(10) \) is found to be approximately 1.812.
### Final Rejection Region
The hypothesis \( H_0 \) is rejected if the computed t-value from the sample data is greater than 1.812. Therefore, the rejection region is:
\[ t > 1.812 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0dffadf4-6195-4ecd-8325-0f00263ddf75%2F9aa8b569-a267-4c9f-b469-1d1b43a1e2fb%2Fatdq2c7_processed.jpeg&w=3840&q=75)
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