1. To test whether a golf ball of brand A can be hit farther off the tee than a golf ball of brand B, each of 12 golfers hit a ball of each brand (six of the golfers hit brand A before brand B, the other six golfers hit brand B prior to brand A). Here are the results: Golfer 1 12 3 4 5 6 7 8 9 10 11 12 Distance for Brand A 245 251 266 254 276 266 243 239 258 260 273 244 Distance for Brand B 253 259 265 274 284 282 279 260 264 290 288 264 Assume that the differences of the paired A distance and B distance are approximately Normally distributed and test the null hypothesis: Hod=0 against the alternative hypothesis, Ha Hd <0 Note: the difference for an individual golfer is defined as: d = Brand A distance Brand B distance Use a paired t-test with a level of significance of a = .10. Be sure to identical the critical region for the test, the degrees of freedom for the test statistics, the value of the test statistic and your conclusion for the test.
1. To test whether a golf ball of brand A can be hit farther off the tee than a golf ball of brand B, each of 12 golfers hit a ball of each brand (six of the golfers hit brand A before brand B, the other six golfers hit brand B prior to brand A). Here are the results: Golfer 1 12 3 4 5 6 7 8 9 10 11 12 Distance for Brand A 245 251 266 254 276 266 243 239 258 260 273 244 Distance for Brand B 253 259 265 274 284 282 279 260 264 290 288 264 Assume that the differences of the paired A distance and B distance are approximately Normally distributed and test the null hypothesis: Hod=0 against the alternative hypothesis, Ha Hd <0 Note: the difference for an individual golfer is defined as: d = Brand A distance Brand B distance Use a paired t-test with a level of significance of a = .10. Be sure to identical the critical region for the test, the degrees of freedom for the test statistics, the value of the test statistic and your conclusion for the test.
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![**Hypothesis Testing for Golf Ball Distances**
**Objective:**
The goal is to evaluate whether a golf ball from Brand A can be hit farther than a golf ball from Brand B. For the experiment, 12 golfers hit a ball from each brand. The order was switched for half of them (six golfers hit Brand A before Brand B, and the others did the opposite).
**Results:**
| Golfer | Distance for Brand A | Distance for Brand B |
|--------|----------------------|----------------------|
| 1 | 245 | 253 |
| 2 | 251 | 259 |
| 3 | 266 | 265 |
| 4 | 254 | 274 |
| 5 | 276 | 284 |
| 6 | 266 | 282 |
| 7 | 243 | 279 |
| 8 | 239 | 260 |
| 9 | 258 | 264 |
| 10 | 260 | 290 |
| 11 | 273 | 288 |
| 12 | 244 | 264 |
**Statistical Hypothesis:**
- **Null Hypothesis (H₀):** The mean difference in distances (Brand A - Brand B) is zero (\( \mu_d = 0 \)).
- **Alternative Hypothesis (Hₐ):** The mean difference in distances is less than zero (\( \mu_d < 0 \)).
**Note:** For each golfer, the difference \( d \) is calculated as:
\[ d = \text{Distance for Brand A} - \text{Distance for Brand B} \]
**Method:**
A paired t-test will be conducted with a significance level \( \alpha = 0.10 \). This involves:
- Identifying the critical region for the test
- Calculating the degrees of freedom
- Determining the test statistic value
- Drawing a conclusion based on the results
This setup provides a framework for students to perform hypothesis testing using real-world data, reinforcing concepts related to statistical comparisons and decision-making.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ad7648d-7881-400e-ae70-2f96519e530b%2F6eb3739c-4b30-486c-a2f1-1ac8fe18e8a3%2Flig290p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing for Golf Ball Distances**
**Objective:**
The goal is to evaluate whether a golf ball from Brand A can be hit farther than a golf ball from Brand B. For the experiment, 12 golfers hit a ball from each brand. The order was switched for half of them (six golfers hit Brand A before Brand B, and the others did the opposite).
**Results:**
| Golfer | Distance for Brand A | Distance for Brand B |
|--------|----------------------|----------------------|
| 1 | 245 | 253 |
| 2 | 251 | 259 |
| 3 | 266 | 265 |
| 4 | 254 | 274 |
| 5 | 276 | 284 |
| 6 | 266 | 282 |
| 7 | 243 | 279 |
| 8 | 239 | 260 |
| 9 | 258 | 264 |
| 10 | 260 | 290 |
| 11 | 273 | 288 |
| 12 | 244 | 264 |
**Statistical Hypothesis:**
- **Null Hypothesis (H₀):** The mean difference in distances (Brand A - Brand B) is zero (\( \mu_d = 0 \)).
- **Alternative Hypothesis (Hₐ):** The mean difference in distances is less than zero (\( \mu_d < 0 \)).
**Note:** For each golfer, the difference \( d \) is calculated as:
\[ d = \text{Distance for Brand A} - \text{Distance for Brand B} \]
**Method:**
A paired t-test will be conducted with a significance level \( \alpha = 0.10 \). This involves:
- Identifying the critical region for the test
- Calculating the degrees of freedom
- Determining the test statistic value
- Drawing a conclusion based on the results
This setup provides a framework for students to perform hypothesis testing using real-world data, reinforcing concepts related to statistical comparisons and decision-making.
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