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) H group. The results are a measure of reduction in back pain. Assume that the two samples are ndependent 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 In 20 20 0.56 0.42 0.95 1.09 ..... OA. Ho: H1 H2 The test statistic, t, is 0.43. (Round to two decimal places as needed.) The P-value is 0.334 . (Round to three decimal places as needed.) State the conclusion for the test. 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. s it valid to argue that magnets might appear to be effective if the sample sizes are larger? Since the sample mean for those treated with magnets is greater than the sample mean for those given a cham treatment, it is valid to argue that magnets might appear to be effective if the sample sizes are larger.
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) H group. The results are a measure of reduction in back pain. Assume that the two samples are ndependent 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 In 20 20 0.56 0.42 0.95 1.09 ..... OA. Ho: H1 H2 The test statistic, t, is 0.43. (Round to two decimal places as needed.) The P-value is 0.334 . (Round to three decimal places as needed.) State the conclusion for the test. 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. s it valid to argue that magnets might appear to be effective if the sample sizes are larger? Since the sample mean for those treated with magnets is greater than the sample mean for those given a cham treatment, it is 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
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I need help with b."construct a confidence interval, suitable for testing the claim...."
![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.
### Statistical Hypotheses:
- **Option C:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 \neq \mu_2 \)
The correct hypothesis choice is:
- **Option D:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 > \mu_2 \)
### Summary Table:
| | Treatment (\(\mu_1\)) | Sham (\(\mu_2\)) |
|-----------|------------------------|------------------|
| \( n \) | 20 | 20 |
| \( \bar{x} \) | 0.56 | 0.42 |
| \( s \) | 0.95 | 1.09 |
### Test Results:
- **Test Statistic (t):** 0.43 (Rounded to two decimal places)
- **P-value:** 0.334 (Rounded to three decimal places)
### 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.
### Consideration of Larger Sample Sizes:
Since the sample mean for those treated with magnets is greater than the sample mean for those given a sham treatment, it is valid to argue that magnets might appear to be effective if the sample sizes are larger.
### Confidence Interval:
Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.
\[ < \mu_1 - \mu_2 < \]
(Round to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb321b15-005b-49cc-ad65-fe2885eda8a3%2F3f8f6746-1f4e-453c-8633-bba03f5a7a73%2Fsxb4vtd_processed.png&w=3840&q=75)
Transcribed Image Text: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.
### Statistical Hypotheses:
- **Option C:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 \neq \mu_2 \)
The correct hypothesis choice is:
- **Option D:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 > \mu_2 \)
### Summary Table:
| | Treatment (\(\mu_1\)) | Sham (\(\mu_2\)) |
|-----------|------------------------|------------------|
| \( n \) | 20 | 20 |
| \( \bar{x} \) | 0.56 | 0.42 |
| \( s \) | 0.95 | 1.09 |
### Test Results:
- **Test Statistic (t):** 0.43 (Rounded to two decimal places)
- **P-value:** 0.334 (Rounded to three decimal places)
### 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.
### Consideration of Larger Sample Sizes:
Since the sample mean for those treated with magnets is greater than the sample mean for those given a sham treatment, it is valid to argue that magnets might appear to be effective if the sample sizes are larger.
### Confidence Interval:
Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.
\[ < \mu_1 - \mu_2 < \]
(Round to three decimal places as needed.)
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