Which one of the following statements is a correct interpretation of the output from the t-test given in Table 1. There is evidence that the underlying mean of BrainChange is negative.It is not plausible that the underlying mean of BrainChange is positive.There is evidence against μNoInt being 0.It is plausible that the underlying mean of BrainChange is 0.It is not plausible that μNoInt is 0. 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 NoIntervention 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 brainooThe 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)NoInterventionooo 0 00 8NoIntervention-1N24O0BrainChangeFigure 1: BrainChange for the NoIntervention groupLet uNoInt be the underlying mean BrainChange when there is no activity assigned.A one-sample t-test with hypotheses Ho: "NoInt = 0 vs H₁ : NoInt 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 Statisticst-.935Odf23OO00 00Mean Std. Deviation Std. Error Mean-.24011.25843.25688One-Sample Test00 OTest 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 Activiand 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.TaiChiSocialNoIntervention00-2BrainChangeTaiChiSocialTotalNoInterventionOFigure 2: BrainChange by ActivityBrainChangeBetween GroupsWithin GroupsTotalO OOD O(1) TreatmentTaiChiSocialOSum ofSquares7.82000NMean29 471127 405624 -2401 1.2584380Std.Deviation.855756969023569896769.55677.376Dependent Variable: BrainChangeTukey HSD(J) TreatmentSocialTaiChiNolnterventionNolntervention TaiChiSocial0 0 0 0Note that one of the values has been replaced with ++Nolntervention0000ANOVADescriptivesdf27779O00000 00Std. Error158911341225688.110658MeanSquare3.910.903000 00⁰ 000BrainChange0Minimum-1.83-1.36-2.03-2.03F++Multiple ComparisonsMean Difference Std.(1-J)Error.06544.25418.71119.26227-.06544.25418.64575.26664-.71119.26227-.64575.26664O co0Maximum2.201.802.012.20Sig..017Sig..964.022.964.046.022.04600000 01O000 0 0O.0844-.6729.0085-1.3380-1.2830O295% Confidence IntervalLower Bound Upper Bound-.5420.67291.3380.54201.2830-.0844-.0085

The question is about hypo. testing From given one sample t test output Test stat ( t ) = -0.935 df…

Answered: Which one of the following statements…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

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Which one of the following statements is a correct interpretation of the output from the t-test given in Table 1.

There is evidence that the underlying mean of BrainChange is negative.
It is not plausible that the underlying mean of BrainChange is positive.
There is evidence against μNoInt being 0.
It is plausible that the underlying mean of BrainChange is 0.
It is not plausible that μNoInt is 0.

Brain size typically shrinks as people age and such shrinkage may be linked to dementia. A study was done in
China to investigate whether different types of activity might help to prevent brain shrinkage or perhaps even lead
to an increase in brain size.
The 80 (non-demented) volunteers were aged between 60 and 69. Each of them had an MRI to determine brain
size before the study began. They were then randomly allocated to one of three activity groups: TaiChi, Social or
Nolntervention.
Except for the Nolntervention group, the groups met with their leaders three times a week over a period of 40
weeks. The NoIntervention 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's
brain 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 a
Community-Based Sample of Non-Demented Chinese Elders.
The two variables used are defined as:
Activity
BrainChange Percentage change in size of participant's brain
oo
The activity the participant was randomly assigned to
- TaiChi
(meet two Tai Chi masters to practise Tai Chi)
- Social
Questions 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)
NoIntervention
ooo 0 00 8
NoIntervention
-1
N
24
O
0
BrainChange
Figure 1: BrainChange for the NoIntervention group
Let uNoInt be the underlying mean BrainChange when there is no activity assigned.
A one-sample t-test with hypotheses Ho: "NoInt = 0 vs H₁ : NoInt 0 was conducted to investigate whether
there was an underlying mean BrainChange when there was no intervention. The output for this test is shown in
Table 1.
One-Sample Statistics
t
-.935
O
df
23
O
O
00 00
Mean Std. Deviation Std. Error Mean
-.2401
1.25843
.25688
One-Sample Test
00 O
Test Value = 0
2
Sig. (2-tailed) Mean Difference
.360
-24012
95% Confidence Interval of the
Lower
-.7715
Difference
Upper
2913

Table 1: One-sample t-test output
Questions 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 Activi
and BrainChange.
Let
Tai be the underlying mean BrainChange
when the activity is TaiChi
"Soc be the underlying mean BrainChange
when the activity is Social
and recall that
"NoInis the underlying mean BrainChange
when there is no activity assigned.
The plot of BrainChange by Activity is shown in Figure 2 (with each group mean being indicated by a
triangle) and the output from the F-test is shown in Table 2.
TaiChi
Social
NoIntervention
00
-2
BrainChange
TaiChi
Social
Total
NoIntervention
O
Figure 2: BrainChange by Activity
BrainChange
Between Groups
Within Groups
Total
O OOD O
(1) Treatment
TaiChi
Social
O
Sum of
Squares
7.820
00
N
Mean
29 4711
27 4056
24 -2401 1.25843
80
Std.
Deviation
.85575
69690
2356
98967
69.556
77.376
Dependent Variable: BrainChange
Tukey HSD
(J) Treatment
Social
TaiChi
Nolntervention
Nolntervention TaiChi
Social
0 0 0 0
Note that one of the values has been replaced with ++
Nolntervention
00
00
ANOVA
Descriptives
df
2
77
79
O
0
00
00 00
Std. Error
15891
13412
25688
.11065
8
Mean
Square
3.910
.903
000 00⁰ 00
0
BrainChange
0
Minimum
-1.83
-1.36
-2.03
-2.03
F
++
Multiple Comparisons
Mean Difference Std.
(1-J)
Error
.06544
.25418
.71119
.26227
-.06544
.25418
.64575
.26664
-.71119
.26227
-.64575
.26664
O co
0
Maximum
2.20
1.80
2.01
2.20
Sig.
.017
Sig.
.964
.022
.964
.046
.022
.046
00
00
0 0
1
O
00
0 0 0
O
.0844
-.6729
.0085
-1.3380
-1.2830
O
2
95% Confidence Interval
Lower Bound Upper Bound
-.5420
.6729
1.3380
.5420
1.2830
-.0844
-.0085

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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