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. H2 29 0.53 0.67 29 0.46 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? A. Ho: H1 = H2 H1: 44 > H2 O B. Ho: H1 H2 H: H1
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. H2 29 0.53 0.67 29 0.46 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? A. Ho: H1 = H2 H1: 44 > H2 O B. Ho: H1 H2 H: H1
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Q3- Hi, please help me find and understand the answer for only the last part of the exercise. Thanks in advance.
Transcribed Image Text:Researchers conducted a study to determine whether magnets are effective in treating back pain. The study compared a treatment group (with magnets) to a sham (placebo) group. The results table measures the reduction in back pain, using independent simple random samples from normally distributed populations, without assuming equal population standard deviations.
### Study Data
- **Treatment (μ₁, n = 29):**
- Mean (x̄) = 0.53
- Standard Deviation (s) = 0.67
- **Sham (μ₂, n = 29):**
- Mean (x̄) = 0.46
- Standard Deviation (s) = 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.**
1. **Null and Alternative Hypotheses**
- Chosen Option A:
- Null Hypothesis (H₀): μ₁ = μ₂
- Alternative Hypothesis (H₁): μ₁ > μ₂
2. **Test Statistic and P-Value**
- Test Statistic, t = 0.30 (rounded to two decimal places)
- P-Value = 0.381 (rounded to three decimal places)
3. **Conclusion**
- **Fail to reject the null hypothesis.** There is not sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.
4. **Validity of Argument**
- It is valid to argue that magnets might appear effective with larger sample sizes since the sample mean for those treated with magnets is greater than the sample mean for the sham group.
**b. Construct a Confidence Interval Suitable for Testing the Claim**
- **Confidence Interval:** `< μ₁ - μ₂ < ` (Rounded to three decimal places as needed)
This study does not provide definitive evidence that magnet treatment is more effective than the sham treatment based on the current data and sample size.
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