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 29 0.56 0.42 0.51 1.03 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 A. Ho: H1 # H2 O B. Ho: H1 = H2 H: H1 # H2 H: H1 H2 The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. V the null hypothesis. There V sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?
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 29 0.56 0.42 0.51 1.03 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 A. Ho: H1 # H2 O B. Ho: H1 = H2 H: H1 # H2 H: H1 H2 The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. V the null hypothesis. There V sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:### Statistical Analysis of Magnet Treatment for Back Pain
Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown for the treatment (with magnets) group and the sham (placebo) group. The results measure the reduction in back pain.
**Table Summary: Treatment vs. Sham**
- **Sample Size (n):** 29 for both groups
- **Mean (\( \bar{x} \)):**
- Treatment: 0.56
- Sham: 0.42
- **Standard Deviation (s):**
- Treatment: 0.51
- Sham: 1.03
#### Hypothesis Testing
**Objective:** 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.
**Possible Null and Alternative Hypotheses:**
- **A.**
- \( H_0: \mu_1 \neq \mu_2 \)
- \( H_1: \mu_1 < \mu_2 \)
- **B.**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 \neq \mu_2 \)
- **C.**
- \( H_0: \mu_1 < \mu_2 \)
- \( H_1: \mu_1 \geq \mu_2 \)
- **D.**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 > \mu_2 \)
**Statistical Testing:**
- The test statistic \( t \) is to be calculated and rounded to two decimal places as needed.
- The P-value should be determined and rounded to three decimal places.
**Conclusion:**
- State the results of the test:
- Either reject or fail to reject the null hypothesis.
- Determine if there is sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.
**Consideration for Larger Sample Sizes:**
- Discuss the validity of arguing the effectiveness of magnets based on larger sample sizes.
This section provides insights into hypothesis testing and data interpretation for determining the effectiveness of treatments using statistical methods.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
