Treatment Sham Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. P2 29 29 0.53 0.46 0.67 1.04 a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses? O B. Ho: H1 #H2 H: H

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Q3- Hi Bartleby team, I'm struggling with this general topic so please provide an answer and a short explanation for all the part of the exercise. Thanks in advance.

**Transcription and Explanation of Statistical Problem on Magnet Treatment for Back Pain**

Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.

---

### Data Table

|               | Treatment (μ₁) | Sham (μ₂)  |
|---------------|----------------|------------|
| Sample Size (n)     | 29             | 29         |
| Sample Mean (x̄)    | 0.53           | 0.46       |
| Sample Standard Deviation (s)| 0.67           | 1.04       |

### Hypothesis Testing

a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses?

- **Option A:**  
  H₀: μ₁ = μ₂  
  H₁: μ₁ > μ₂

- **Option B:**  
  H₀: μ₁ ≠ μ₂  
  H₁: μ₁ < μ₂

- **Option C:**  
  H₀: μ₁ < μ₂  
  H₁: μ₁ ≥ μ₂

- **Option D:**  
  H₀: μ₁ ≠ μ₂  
  H₁: μ₁ ≠ μ₂

### Statistical Calculation

- **The test statistic, t, is** _____ (Round to two decimal places as needed.)
- **The P-value is** _____ (Round to three decimal places as needed.)
Transcribed Image Text:**Transcription and Explanation of Statistical Problem on Magnet Treatment for Back Pain** Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. --- ### Data Table | | Treatment (μ₁) | Sham (μ₂) | |---------------|----------------|------------| | Sample Size (n) | 29 | 29 | | Sample Mean (x̄) | 0.53 | 0.46 | | Sample Standard Deviation (s)| 0.67 | 1.04 | ### Hypothesis Testing a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses? - **Option A:** H₀: μ₁ = μ₂ H₁: μ₁ > μ₂ - **Option B:** H₀: μ₁ ≠ μ₂ H₁: μ₁ < μ₂ - **Option C:** H₀: μ₁ < μ₂ H₁: μ₁ ≥ μ₂ - **Option D:** H₀: μ₁ ≠ μ₂ H₁: μ₁ ≠ μ₂ ### Statistical Calculation - **The test statistic, t, is** _____ (Round to two decimal places as needed.) - **The P-value is** _____ (Round to three decimal places as needed.)
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