The current epidemic of opioid addiction has led researchers to search for alternative therapies for pain reduction. Chronic lower back pain is one of the most common conditions that routinely receive opioid therapy, despite limited evidence that such therapy is effective in lowering pain levels. Researchers conduct a study to determine if regular yoga can lead to similar effects on pain levels compared to opioid therapy. Twenty-five patients (group 1) with chronic lower back pain receive six months of opioid therapy and at the end of the six months have a mean pain level of 15.7 with a sample standard deviation of 4.3. A separate group of 25 patients (group 2) with chronic lower back pain received six months of daily yoga sessions and after six months have a mean pain level of 9.8 with a sample standard deviation of 4.0. We can assume that the population variances in the two groups are equal. We want to test the claim that the pain levels of people on regular yoga therapy are different from the pain levels of people receiving opioid therapy at a significance level of 0.05.

What is the most appropriate test for the given claim? What formula to use?

What is the null hypothesis and alternative hypothesis?