2 **Research Study on the Effectiveness of Magnets for Back Pain Relief**Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are presented in a table comparing a treatment group (using magnets) and a sham (placebo) group. The results measure the reduction in back pain. Assume the samples are independent simple random samples from normally distributed populations and that population standard deviations are not equal. Analyze the following tasks:### Data Summary| Treatment (Magnets) | Sham (Placebo) ||---------------------|----------------|| 0.76 | 1.53 || 1.14 | 0.93 || 0.72 | 1.05 |### Statistical Analysis Tasks**a. Significance Test at 0.05 Level**Test whether individuals treated with magnets report a greater mean reduction in pain compared to those given a sham treatment.- **Hypothesis Statements:** - Option A: \( H_0: \mu_1 = \mu_2 \) vs. \( H_1: \mu_1 \neq \mu_2 \) - Option B: \( H_0: \mu_1 = \mu_2 \) vs. \( H_1: \mu_1 < \mu_2 \) - Option C: \( H_0: \mu_1 = \mu_2 \) vs. \( H_1: \mu_1 > \mu_2 \) - Option D: \( H_0: \mu_1 = \mu_2 \) vs. \( H_1: \mu_1 \geq \mu_2 \)- **Test Statistic:** - Calculate and enter the test statistic \( t \) value. (Round to two decimal places)- **P-Value:** - Calculate and enter the P-value. (Round to three decimal places)- **Conclusion:** - State whether to reject or fail to reject the null hypothesis. There is or isn't sufficient evidence to support the claim that those treated with magnets show a greater reduction in pain than those given a sham treatment.**b. Sample Size Consideration**- Discuss the validity of using the magnet treatment results given a small sample size and whether the results might appear more valid with a larger sample size.**c. Confidence Interval Construction**- Construct a

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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. e null and altemative hypotheses? OB. H P2 OD. Hi "2 statistic, t is (Round to two decimal places as needed) value is (Round to three decimal places as needed.) the condusion for the test Vthe nul 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. valid to argue that magnets might appear to be effective if the sample sizes are larger? nce the V for those treated with magnets is v the sample mean for those given a sham treatment, it v valid to argue that magnets might appear to be effective if the sample sizes are larger. 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. Round to three decimal places as needed.)