Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. 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) to (c) below. Reduction in Pain Level After Magnet Treatment (4,): n = 29, x= 0.59, s = 0.99 Reduction in Pain Level After Sham Treatment (42): n = 29, x = 0.54, s = 1.46 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 (similar to a placebo). What are the null and alternative hypotheses? O A. Ho: H1 = H2 O B. Ho: H1 H2 대>H : H C. Ho: H1= H2 H: H > H2 O D. Ho: H1

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I need help finding the test statistic t (rounded to 2 decimal places) and the P-value (rounded to 3 decimal places). Thank you

In a study conducted by researchers, the effectiveness of magnets in treating back pain was assessed. Pain levels were measured using a visual analog scale, where higher scores indicate greater pain. The data provided are as follows:

1. **Reduction in Pain Level After Magnet Treatment (\( \mu_1 \)):**
   - Sample size (\( n \)): 29
   - Mean (\( \bar{x} \)): 0.59
   - Standard deviation (\( s \)): 0.99

2. **Reduction in Pain Level After Sham Treatment (\( \mu_2 \)):**
   - Sample size (\( n \)): 29
   - Mean (\( \bar{x} \)): 0.54
   - Standard deviation (\( s \)): 1.46

The study aims to test whether magnet treatment results in a greater mean reduction in pain compared to sham treatment (a placebo effect).

**Statistical Testing:**

Using a 0.05 significance level, the hypotheses to be tested are:

- **Null Hypothesis (\( H_0 \))**: \( \mu_1 = \mu_2 \)
- **Alternative Hypothesis (\( H_1 \))**: \( \mu_1 \neq \mu_2 \)

The correct choices for the hypotheses are indicated as:

- **Option C**: \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 \neq \mu_2 \)

**Instructions:**

The test statistic \( t \) needs to be calculated. Results should be rounded to two decimal places as required.
Transcribed Image Text:In a study conducted by researchers, the effectiveness of magnets in treating back pain was assessed. Pain levels were measured using a visual analog scale, where higher scores indicate greater pain. The data provided are as follows: 1. **Reduction in Pain Level After Magnet Treatment (\( \mu_1 \)):** - Sample size (\( n \)): 29 - Mean (\( \bar{x} \)): 0.59 - Standard deviation (\( s \)): 0.99 2. **Reduction in Pain Level After Sham Treatment (\( \mu_2 \)):** - Sample size (\( n \)): 29 - Mean (\( \bar{x} \)): 0.54 - Standard deviation (\( s \)): 1.46 The study aims to test whether magnet treatment results in a greater mean reduction in pain compared to sham treatment (a placebo effect). **Statistical Testing:** Using a 0.05 significance level, the hypotheses to be tested are: - **Null Hypothesis (\( H_0 \))**: \( \mu_1 = \mu_2 \) - **Alternative Hypothesis (\( H_1 \))**: \( \mu_1 \neq \mu_2 \) The correct choices for the hypotheses are indicated as: - **Option C**: \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 \neq \mu_2 \) **Instructions:** The test statistic \( t \) needs to be calculated. Results should be rounded to two decimal places as required.
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