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(b) Give the notation for the sample statistic. :: ⠀⠀ :: μ μ4₁ :: T₂ :: p 1₂ :: p :: P₁ :: P₁ :: P₂ :: P₂ r T p :: T :: I₁

(b) Give the notation for the sample statistic. :: ⠀⠀ :: μ μ4₁ :: T₂ :: p 1₂ :: p :: P₁ :: P₁ :: P₂ :: P₂ r T p :: T :: I₁

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(b) Give the notation for the sample statistic. II Sample statistic: # Value = i :: < Enter the exact answer. (c) Give the value for the sample statistic. p-value = i # fl IT :: £₂ 4 ::H₂ p (d) Use the randomization distribution to estimate the p-value. Round your answer to three decimal places. A P₁ p P₁ A :: P₂ :: P2 r T p :: I₁
Transcribed Image Text:(b) Give the notation for the sample statistic. II Sample statistic: # Value = i :: < Enter the exact answer. (c) Give the value for the sample statistic. p-value = i # fl IT :: £₂ 4 ::H₂ p (d) Use the randomization distribution to estimate the p-value. Round your answer to three decimal places. A P₁ p P₁ A :: P₂ :: P2 r T p :: I₁
If You Break an Arm, Use Your Brain! Multiple studies are helping us understand the power of the mind on the body. One such study¹ examines 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. 30 20 10 0 -30 Ho: ***. : -25 -20 (a) State the null and alternative hypotheses. -15 < :: μ -10 vs Ha: μ₁1 milita T2 -5 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. :: p 1₂ null = 0 A :: P₁ p 5 A :: P₂ 10 :: P₁ :: P2 ⠀r 15 T LA .. p 20 25
Transcribed Image Text:If You Break an Arm, Use Your Brain! Multiple studies are helping us understand the power of the mind on the body. One such study¹ examines 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. 30 20 10 0 -30 Ho: ***. : -25 -20 (a) State the null and alternative hypotheses. -15 < :: μ -10 vs Ha: μ₁1 milita T2 -5 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. :: p 1₂ null = 0 A :: P₁ p 5 A :: P₂ 10 :: P₁ :: P2 ⠀r 15 T LA .. p 20 25
Expert Solution
Step 1

Given:-

            n1 =  15 participants not using any mental imagery.

n2 =14 participants not using any mental imagery.

μ1 = 51.2

μ2 = 24.5

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