Question

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. Use a 0.05 significance level for both parts.

Treatment: µ=µ1; n=14; x=0.48; s=0.61

Sham treatment: µ=µ2; n=14; x=0.36; s=1.38

H0: µ1=µ2

H1: µ1≠µ2

T = 0.30

P-value = 0.383

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. (solve below)

__ < µ1 - µ2 < __

Answer 1

For testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment, we have:

H0: $\mu1\leq\mu2$ =$\mu1-\mu2\leq0$

H1: $\mu1>\mu2$ =$\mu1-\mu2>0$ (right tailed test)

Now, we need one sided 95% confidence interval(CI) for the difference in means.

Critical value of t is:

Lower bound =$-\propto$ (negative infinite)

Upper bound =$(\bar{X1} - \bar{X2})\pm t.\sqrt{(s1^2/n1)&plus; (s2^2/n2)}$​​​​​​

=(0.48-0.36)$\pm 1.734.\sqrt{(0.61^2/14)&plus; (1.38^2/14)}$ =0.82

Thus, one sided (right tailed) 95% CI for $\mu1-\mu2$ =(-$\propto$​​​​​​, 0.82)

Hence, $-\propto$ < $\mu1-\mu2$ < 0.82