Which one of the following statements is false? With 95% confidence, we estimate thatμNoInt is somewhere between -0.77 and 0.29.On average, the brain size of the participants in the NoIntervention group decreased.x¯NoInt=−0.24.The estimate, x¯NoInt, is 0.94 standard errors below the hypothesised value of 0.The margin of error is 0.26. Brain size typically shrinks as people age and such shrinkage may be linked to dementia. A study was done inChina to investigate whether different types of activity might help to prevent brain shrinkage or perhaps even leadto an increase in brain size.The 80 (non-demented) volunteers were aged between 60 and 69. Each of them had an MRI to determine brainsize before the study began. They were then randomly allocated to one of three activity groups: TaiChi, Social orNolntervention.Except for the Nolntervention group, the groups met with their leaders three times a week over a period of 40weeks. The Nolntervention group were called four times by the study coordinator during the study period.At the end of the study, the participants had another MRI and the percentage change in size of each participant'sbrain was calculated.Adapted from: Mortimer, J. A., Ding, D., Borenstein, A. R., DeCarli C., Guo, Q., Wu, Y., Zhao, Q. and Chu, S.(2012), Changes in Brain Volume and Cognition in a Randomized Trial of Exercise and Social Interaction in aCommunity-Based Sample of Non-Demented Chinese Elders.The two variables used are defined as:ActivityBrainChange Percentage change in size of participant's brain00The activity the participant was randomly assigned to- TaiChi(meet two Tai Chi masters to practise Tai Chi)- SocialQuestions 8 and 9 refer to the following additional information.-2(meet at a community centre to discuss interesting topics)- NoIntervention(no activity assigned)A plot of BrainChange for the participants who were assigned to the Nolntervention group is shown in Figure 1.The mean is indicated by the triangle.(where a positive value means the brain increased in size)ooo oo oo 8NoInterventionNoInterventionBrainChangeFigure 1: BrainChange for the NoIntervention groupO OOLet μNoInt be the underlying mean BrainChange when there is no activity assigned.A one-sample t-test with hypotheses Ho: "NoInt=0 vs H₁ μNoInt 0 was conducted to investigate whetherthere was an underlying mean BrainChange when there was no intervention. The output for this test is shown inTable 1.One-Sample StatisticsN24t-93500 00df23Mean Std. Deviation Std. Error Mean-.24011.2584325688One-Sample Test00Test Value = 02Sig. (2-tailed) Mean Difference.360-2401295% Confidence Interval of theLower-.7715DifferenceUpper2913 Table 1: One-sample t-test outputQuestions 10 to 14 refer to the following additional information.A one-way analysis of variance (ANOVA) F-test was conducted to investigate the relationship between Activityand BrainChange.LetTai be the underlying mean BrainChangewhen the activity is TaiChi"Soc be the underlying mean BrainChangewhen the activity is Socialand recall that"NoInis the underlying mean BrainChangewhen there is no activity assigned.The plot of BrainChange by Activity is shown in Figure 2 (with each group mean being indicated by atriangle) and the output from the F-test is shown in Table 2.TaiChiSocialNoIntervention00-2BrainChangeTotalTaiChiSocialNoInterventionOBrainChangeBetween GroupsWithin GroupsTotalFigure 2: BrainChange by ActivityOO(1) TreatmentTaiChiSocialO-1N2927 405624 - 240180 2356Mean4711Sum ofSquares7.82069.55677.37600(J) TreatmentSocialTaiChiDependent Variable: BrainChangeTukey HSDNolntervention TaiChiSocial0 0 0 0Note that one of the values has been replaced with ++NoInterventionNoIntervention00.85575696901.2584398967ANOVADescriptivesOStd.Deviation Std. Errordf27779O00 00O00158911341225688110650BrainChangeMeanSquare3.910.9038 000 00⁰ 0.0Mean Difference(I-J).06544.71119-.06544.64575-.71119-.64575Minimum-1.83-1.36-2.03-2.03Multiple ComparisonsF++Std.Error.25418.26227.25418.26664.26227.266640 00 0OMaximum2.201.802.012.20Sig.0170000OO O 001O0 0 0O.0844-.6729.0085-1.3380-1.2830OO295% Confidence IntervalSig. Lower Bound Upper Bound.964-.5420.6729.0221.3380.964.5420.0461.2830.022-.0844.046-.0085O

Given the results of the study done in China to investigate whether different types of activity…

Which one of the following statements is false? With 95% confidence, we estimate thatμNoInt is somewhere between -0.77 and 0.29. On average, the brain size of the participants in the NoIntervention group decreased. x¯NoInt=−0.24. The estimate, x¯NoInt, is 0.94 standard errors below the hypothesised value of 0. The margin of error is 0.26.

Which one of the following statements is false? With 95% confidence, we estimate thatμNoInt is somewhere between -0.77 and 0.29. On average, the brain size of the participants in the NoIntervention group decreased. x¯NoInt=−0.24. The estimate, x¯NoInt, is 0.94 standard errors below the hypothesised value of 0. The margin of error is 0.26.

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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