Reject or Fail to Reject the null hypothesis. There is or 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. The image shows a statistical analysis exercise related to the effectiveness of magnets in treating back pain.### Instructions:1. **Test Statistic Calculation:** - The test statistic, `t`, is _______. (Round to two decimal places as needed.) 2. **P-Value Calculation:** - The P-value is _______. (Round to three decimal places as needed.) 3. **Conclusion for the Test:** - □ Reject - □ Fail to reject the null hypothesis. There □ is □ 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. **Confidence Interval:** - Construct a confidence interval appropriate for the hypothesis test. \(\mu_1 - \mu_2 \) (Round to two decimal places as needed.)### Multiple Choice Questions:#### c. Evaluation of Magnets' Effectiveness:1. **Does it appear that magnets are effective in treating back pain?** - A. It appears that magnets are not effective in treating back pain, because 0 is in the confidence interval. - B. It appears that magnets are effective in treating back pain, because the P-value is greater than the significance level. - C. It appears that magnets are not effective in treating back pain, because the P-value is less than the significance level. - D. It appears that magnets are effective in treating back pain, because the confidence interval contains only positive values.2. **Is it valid to argue that magnets might appear to be more effective if the sample sizes are larger?** - A. Yes, because increasing the sample size will decrease the P-value. - B. No, because the magnets already appear to be effective. - C. No, because increasing the sample size will increase the P-value. - D. Yes, because increasing the sample size will increase the effectiveness.Note: The above includes placeholders for statistical values and steps that require calculation; ensure these computations are carried out accurately for proper interpretation and analysis. **Study on the Effectiveness of Magnets in Treating Back Pain**Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, with higher scores corresponding to greater pain levels. Below are the results obtained from the study. Assume that the two samples are independent simple random samples selected from normally distributed populations, and that the population standard deviations are not assumed to be equal.- **Reduction in Pain Level After Magnet Treatment (\( \mu_1 \)):** - Sample Size (\( n \)): 15 - Mean (\( \bar{x} \)): 0.55 - Standard Deviation (\( s \)): 0.95- **Reduction in Pain Level After Sham Treatment (\( \mu_2 \)):** - Sample Size (\( n \)): 15 - Mean (\( \bar{x} \)): 0.51 - Standard Deviation (\( s \)): 1.43---**Hypothesis Testing**a. Use a 0.01 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo).**What are the null and alternative hypotheses?****Options:**- **A.** - \( H_0: \mu_1 \ne \mu_2 \) - \( H_1: \mu_1 < \mu_2 \)- **B.** - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 > \mu_2 \)- **C.** - \( H_0: \mu_1 < \mu_2 \) - \( H_1: \mu_1 \ge \mu_2 \)- **D.** - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 \ne \mu_2 \)

Given that: Reduction in Pain Level After Magnet Treatment: n1=15x¯1=0.55s1=0.95 Reduction in Pain…

Answered: Researchers conducted a study to…

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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Reject or Fail to Reject the null hypothesis. There is or 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.

The image shows a statistical analysis exercise related to the effectiveness of magnets in treating back pain.

### Instructions:
1. **Test Statistic Calculation:**
- The test statistic, `t`, is _______. (Round to two decimal places as needed.)

2. **P-Value Calculation:**
- The P-value is _______. (Round to three decimal places as needed.)

3. **Conclusion for the Test:**
- □ Reject
- □ Fail to reject

the null hypothesis. There □ is □ 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. **Confidence Interval:**
- Construct a confidence interval appropriate for the hypothesis test.
\(\mu_1 - \mu_2 \)
(Round to two decimal places as needed.)

### Multiple Choice Questions:

#### c. Evaluation of Magnets' Effectiveness:

1. **Does it appear that magnets are effective in treating back pain?**
- A. It appears that magnets are not effective in treating back pain, because 0 is in the confidence interval.
- B. It appears that magnets are effective in treating back pain, because the P-value is greater than the significance level.
- C. It appears that magnets are not effective in treating back pain, because the P-value is less than the significance level.
- D. It appears that magnets are effective in treating back pain, because the confidence interval contains only positive values.

2. **Is it valid to argue that magnets might appear to be more effective if the sample sizes are larger?**
- A. Yes, because increasing the sample size will decrease the P-value.
- B. No, because the magnets already appear to be effective.
- C. No, because increasing the sample size will increase the P-value.
- D. Yes, because increasing the sample size will increase the effectiveness.

Note: The above includes placeholders for statistical values and steps that require calculation; ensure these computations are carried out accurately for proper interpretation and analysis.

**Study on the Effectiveness of Magnets in Treating Back Pain**

Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, with higher scores corresponding to greater pain levels. Below are the results obtained from the study. Assume that the two samples are independent simple random samples selected from normally distributed populations, and that the population standard deviations are not assumed to be equal.

- **Reduction in Pain Level After Magnet Treatment (\( \mu_1 \)):**
- Sample Size (\( n \)): 15
- Mean (\( \bar{x} \)): 0.55
- Standard Deviation (\( s \)): 0.95

- **Reduction in Pain Level After Sham Treatment (\( \mu_2 \)):**
- Sample Size (\( n \)): 15
- Mean (\( \bar{x} \)): 0.51
- Standard Deviation (\( s \)): 1.43

---

**Hypothesis Testing**

a. Use a 0.01 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo).

**What are the null and alternative hypotheses?**

**Options:**

- **A.**
- \( H_0: \mu_1 \ne \mu_2 \)
- \( H_1: \mu_1 < \mu_2 \)

- **B.**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 > \mu_2 \)

- **C.**
- \( H_0: \mu_1 < \mu_2 \)
- \( H_1: \mu_1 \ge \mu_2 \)

- **D.**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 \ne \mu_2 \)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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