Multiple studies are helping us understand the power of the mind on the body. One such study1examines the effect of imagery on muscle strength. In the study, 29 healthy individuals underwent four weeks of wrist immobilization to induce weakness. Half of the participants were randomly assigned to mentally imagine strong muscle contractions in that arm (without actually moving the arm.) At the end of the four weeks, the percentage decrease in muscle strength was measured for all the participants, and we are testing to see if mean decrease is greater for people who do not use mental imaging when muscles are immobilized than for people who do. For the 15 participants not using any mental imagery, the mean percent decrease in muscle strength was 51.2 while for the 14 participants using imagery, it was 24.5. A randomization distribution of differences in means (mean decrease with no imagery minus mean decrease with imagery) using 1000 simulated samples is shown in the figure below.
Let group 1 be those who do no imagery and let group 2 be those who do imagery. 1Clark BC, et al., "The power of the mind: the cortex as a critical determinant of muscle strength/weakness," J Neurophysiol, 112: 32193226, October 2014.
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(a) State the null and alternative hypotheses.
(b) Give the notation for the sample statistic.
(c) Give the value for the sample statistic.
(d) Use the randomization distribution to estimate the p-value.

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From the given information Let n 1 15 represent the number of participants not using any mental imag... View the full answer