Researchers conducted a study to determine whether magnets are effective in trea

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. Complete parts? (a) and? (b) below. Treatment Sham ? ?1 ?2 n 27 27 x 0.53 0.41 s 0.84 1.14 a. Use a 0.05 significance? level, and test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. 1. What are the null and alternative? hypotheses? A. H0?: ?1= ?2 H1?: ?1? ?2 B. H0?: ?1 < ?2 H1?: ?1 ? ?2 C. H0?: ?1 = ?2 H1?: ?1 > ?2 D. H0?: ?1 ? ?2 H1?: ?1< ?2 2. The test? statistic,is ______ ?(Round to two decimal places as? needed.) 3. The? P-value is ______ ?(Round to three decimal places as? needed.) 4. State the conclusion for the test. ________________ the null hypothesis. There ______ sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. 5. Is it valid to argue that magnets might appear to be effective if the sample sizes are? larger? Since the ___________ for those treated with magnets is _________ the sample mean for those given a sham? treatment, it ___________ valid to argue that magnets might appear to be effective if the sample sizes are larger. b. 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. ____< ?1??2 < ______ ?(Round to three decimal places as? needed.)

Explanation / Answer

as we are interested in "greater mean reduction" part of the question , hence it becomes a 1 tail right t test so the correct hypothesis is

C. H0?: ?1 = ?2

H1?: ?1 > ?2

Standard error. Compute the standard error (SE) of the sampling distribution.
SE = sqrt[ (s12/n1) + (s22/n2) ]

putting the values we get
sqrt( (0.84^2)/27 + (1.14^2)/27) = 0.2725

Test statistic. The test statistic is a t statistic (t) defined by the following equation.
t = [ (x1 - x2) - d ] / SE

t = (0.53-0.41)/0.2725 = 0.4403

Degrees of freedom. The degrees of freedom (DF) is:
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }

If DF does not compute to an integer, round it off to the nearest whole number. Some texts suggest that the degrees of freedom can be approximated by the smaller of n1 - 1 and n2 - 1; but the above formula gives better results.

df = ( (0.84^2)/27 + (1.14^2)/27) / ((((0.84^2)/27)^2 / (27 - 1) ) + ( ((1.14^2)/27)^2 / (27 - 1) )) = 643.69 ~ 644

now we check the t table for the p value , please keep the t table handy (or a calculator)
with
alpha = 0.05 and df = 644
The P-Value is o.329934.

The result is not significant at p < .05.

4. State the conclusion for the test.

fail to reject the null hypothesis. There __is no____ sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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