LINK TO TEXT (b) What is the sample mean difference in inflammation between no m
ID: 3328654 • Letter: L
Question
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(b) What is the sample mean difference in inflammation between no massage and massage?
exact number, no tolerance
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(c) We want to test to see if the population mean difference D is greater than zero, meaning muscle with no treatment has more inflammation than muscle that has been massaged.
State the null and alternative hypotheses.
Use instead of D to answer this question.
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(d) Use StatKey or other technology to find the p-value from a randomization distribution.
Round your answer to three decimal places.
the absolute tolerance is +/-0.01
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Does Massage Help Heal Muscles Strained by Exercise?After exercise, massage is often used to relieve pain, and a recent study1 shows that it also may relieve inflammation and help muscles heal. In the study, eleven male participants who had just strenuously exercised had 10 minutes of massage on one quadricep and no treatment on the other, with treatment randomly assigned. After 2.5 hours, muscle biopsies were taken and production of the inflammatory cytokine interleukin-6 was measured relative to the resting level. The differences (control minus massage) are given in Table 1 below. 0.6 4.7 3.8 0.4 1.5 -1.2 2.8 -0.4 1.4 3.5 -2.8
Table 1: Inflammation in muscle: control minus massage
1Data approximated from summary statistics in Crane, et.al., "Massage Therapy Attenuates Inammatory Signaling After Exercise-Induced Muscle Damage", Science Translational Medicine, 1 February 2012.
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Explanation / Answer
(1) THe given study is an experiment study.
(2) sample mean difference dbar = sum of all differences/ 11 = 1.3
(3) Null Hypothesis : Ho : There is no difference in inflammation caused by massage. = 0
Alternative Hypothesis : Ha : There are significant increase in inflammation caused by massage. > 0
(4) Standard deviation of the mean difference sd = 2.285
It can be calculated by the formula = 1/ (n-1) (d - dbar)2
test statistic
t = / (sd / sqrt(n) )
t = 1.3 / (2.285/ sqrt(11))
t = 1.89
so critical test statistic
for dF = 10 and alpha = 0.05 and 0.01
tcr (alpha = 0.05) = 2.228
tcr (alpha = 0.01) = 3.169
so here t < tcr (0.05) and t < tcr (0.01)
so in both cases, we cannot reject the null hypothesis . Do not reject H0, there is no evidence that massage makes a difference. Option D is correct.
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