ТуреABReplacedRepairedNot ReturnedC12361087829658there seem to be a significant difference among the reliabilities of the different radioDoesIfso, which ones seem to be different?types?The amount of iron present in the livers of white rats is measured after the animals hadbeen fed one of five diets for a prescribed length of time. There were 10 animals randomly5.assigned to each of the five diets.orandsDiet ADiet BDiet CDiet DDiet E2.235.594.501.35were1.401.140.96under3.921.061.512.636.96nked10.330.742.49those1.001.238.230.961.74TA C21.351.612.071.161.592.012.944.902.081.36pecou gmboa*d1.641.966.840.693.001.133.686.424.810.681.541.013.725.210.841.702.595.126.001.34Do the different diets appear to affect the amount of iron present in the livers?Twelve volunteers were assigned to each of three weight-reducing plans. The assignments?6.of the volunteers to the plans was at random, and it was assumed that the 36 volunteersin all would resemble a random sample of people who might try a weight-reducingprogram. Test the null hypothesis that there is no difference in the probability distributionsof the amount of weight lost under the three programs against the alternative that thereis a difference. The results are given as the number of pounds lost by each person.orisPlan CPlan BPlan A517 5 291722515 6 325412323 1925528 244194 69 b11 36521266 14 7 7 20e r8brs !nPROBLEMSShow that Equations 3 and 5 are equivalent when there are no ties.Find the exact distribution of the Kruskal-Wallis test statistic when Ho is true, n1 3, i=1,2, . . . ,kj-1(2)Compute Ri for each sample.If the ranks may be assigned in several different ways because severalobservations are equal to each other, assign the average rank to each of the tiedobservations, as in the previous test of this chapter.ewAssumptions1. All samples are random samples from their respective populations.9r2. In addition to independence within each sample, there is mutual indepen-dence among the various samples.The measurement scale is at least ordinal.4. Either the k population distribution functions are identical, or else some ofthe populations tend to yield larger values than other populations do.Test StatisticThe test statistic T is defined1ecpeonn.odalnqo exingsbjanR N(N+ 12T-3(3)bac4d iina aib sdniBwhere N and Ri are defined in Equations 1 and 2, respectively, and whereS2 1N 12R(Xj)2- N(N+ 1)24(4)-8.eslorns w!0eallranksV4AIRA eldeT51+AIf there are no ties S2 simplifies to N(N + 1)/12, and the test statistic reduces tosvynu 2sR2- 3(N+ 1)12(5)T=N(N+ 1)e-8If the number of ties is moderate there will be very little difference betweenEquations 3 and 5, so the simpler Equation 5 may be preferred.Null Distribution The exact distribution of T is given by Table A8 for k = 3 andall ni s 5, but in general the exact distribution is too cumbersome to work with.Therefore the chi-squared distribution with k - 1 degrees of freedom is used asan approximation to the null distribution of T.

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Asked Nov 20, 2019
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Problem 1 in images. Equations (3) and Equations(5) is give in the second image , it’s under the bold Title Test Statistic on the right it says (3) and the same for equation 5, it’s noted by (5)

Туре
A
B
Replaced
Repaired
Not Returned
C
12
3
6
10
8
7
82
96
58
there seem to be a significant difference among the reliabilities of the different radio
Does
If
so, which ones seem to be different?
types?
The amount of iron present in the livers of white rats is measured after the animals had
been fed one of five diets for a prescribed length of time. There were 10 animals randomly
5.
assigned to each of the five diets.
orands
Diet A
Diet B
Diet C
Diet D
Diet E
2.23
5.59
4.50
1.35
were
1.40
1.14
0.96
under
3.92
1.06
1.51
2.63
6.96
nked
10.33
0.74
2.49
those
1.00
1.23
8.23
0.96
1.74
TA C2
1.35
1.61
2.07
1.16
1.59
2.01
2.94
4.90
2.08
1.36
pecou gm
boa*d
1.64
1.96
6.84
0.69
3.00
1.13
3.68
6.42
4.81
0.68
1.54
1.01
3.72
5.21
0.84
1.70
2.59
5.12
6.00
1.34
Do the different diets appear to affect the amount of iron present in the livers?
Twelve volunteers were assigned to each of three weight-reducing plans. The assignment
s?
6.
of the volunteers to the plans was at random, and it was assumed that the 36 volunteers
in all would resemble a random sample of people who might try a weight-reducing
program. Test the null hypothesis that there is no difference in the probability distributions
of the amount of weight lost under the three programs against the alternative that there
is a difference. The results are given as the number of pounds lost by each person.
or
is
Plan C
Plan B
Plan A
5
17 5 29
17
2
25
15 6 3
25
4
12
32
3 19
25
5
28 24
4
19
4 6
9 b11 36
5
21
26
6 14 7 7 20
e r
8
brs !n
PROBLEMS
Show that Equations 3 and 5 are equivalent when there are no ties.
Find the exact distribution of the Kruskal-Wallis test statistic when Ho is true, n1 3,
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Туре A B Replaced Repaired Not Returned C 12 3 6 10 8 7 82 96 58 there seem to be a significant difference among the reliabilities of the different radio Does If so, which ones seem to be different? types? The amount of iron present in the livers of white rats is measured after the animals had been fed one of five diets for a prescribed length of time. There were 10 animals randomly 5. assigned to each of the five diets. orands Diet A Diet B Diet C Diet D Diet E 2.23 5.59 4.50 1.35 were 1.40 1.14 0.96 under 3.92 1.06 1.51 2.63 6.96 nked 10.33 0.74 2.49 those 1.00 1.23 8.23 0.96 1.74 TA C2 1.35 1.61 2.07 1.16 1.59 2.01 2.94 4.90 2.08 1.36 pecou gm boa*d 1.64 1.96 6.84 0.69 3.00 1.13 3.68 6.42 4.81 0.68 1.54 1.01 3.72 5.21 0.84 1.70 2.59 5.12 6.00 1.34 Do the different diets appear to affect the amount of iron present in the livers? Twelve volunteers were assigned to each of three weight-reducing plans. The assignment s? 6. of the volunteers to the plans was at random, and it was assumed that the 36 volunteers in all would resemble a random sample of people who might try a weight-reducing program. Test the null hypothesis that there is no difference in the probability distributions of the amount of weight lost under the three programs against the alternative that there is a difference. The results are given as the number of pounds lost by each person. or is Plan C Plan B Plan A 5 17 5 29 17 2 25 15 6 3 25 4 12 32 3 19 25 5 28 24 4 19 4 6 9 b11 36 5 21 26 6 14 7 7 20 e r 8 brs !n PROBLEMS Show that Equations 3 and 5 are equivalent when there are no ties. Find the exact distribution of the Kruskal-Wallis test statistic when Ho is true, n1 3,

fullscreen
i=1,2, . . . ,k
j-1
(2)
Compute Ri for each sample.
If the ranks may be assigned in several different ways because several
observations are equal to each other, assign the average rank to each of the tied
observations, as in the previous test of this chapter.
ew
Assumptions
1. All samples are random samples from their respective populations.
9r2. In addition to independence within each sample, there is mutual indepen-
dence among the various samples.
The measurement scale is at least ordinal.
4. Either the k population distribution functions are identical, or else some of
the populations tend to yield larger values than other populations do.
Test Statistic
The test statistic T is defined
1ecpeonn.
odalnqo exing
sbjan
R N(N+ 12
T-3
(3)
bac
4
d iina aib sd
ni
B
where N and Ri are defined in Equations 1 and 2, respectively, and where
S2 1
N 1
2R(Xj)2- N(N+ 1)2
4
(4)
-8.eslorns w!
0e
all
ranks
V4A
IRA eldeT
51+A
If there are no ties S2 simplifies to N(N + 1)/12, and the test statistic reduces to
svy
nu 2s
R2
- 3(N+ 1)
12
(5)
T=
N(N+ 1)
e
-8
If the number of ties is moderate there will be very little difference between
Equations 3 and 5, so the simpler Equation 5 may be preferred.
Null Distribution The exact distribution of T is given by Table A8 for k = 3 and
all ni s 5, but in general the exact distribution is too cumbersome to work with.
Therefore the chi-squared distribution with k - 1 degrees of freedom is used as
an approximation to the null distribution of T.
help_outline

Image Transcriptionclose

i=1,2, . . . ,k j-1 (2) Compute Ri for each sample. If the ranks may be assigned in several different ways because several observations are equal to each other, assign the average rank to each of the tied observations, as in the previous test of this chapter. ew Assumptions 1. All samples are random samples from their respective populations. 9r2. In addition to independence within each sample, there is mutual indepen- dence among the various samples. The measurement scale is at least ordinal. 4. Either the k population distribution functions are identical, or else some of the populations tend to yield larger values than other populations do. Test Statistic The test statistic T is defined 1ecpeonn. odalnqo exing sbjan R N(N+ 12 T-3 (3) bac 4 d iina aib sd ni B where N and Ri are defined in Equations 1 and 2, respectively, and where S2 1 N 1 2R(Xj)2- N(N+ 1)2 4 (4) -8.eslorns w! 0e all ranks V4A IRA eldeT 51+A If there are no ties S2 simplifies to N(N + 1)/12, and the test statistic reduces to svy nu 2s R2 - 3(N+ 1) 12 (5) T= N(N+ 1) e -8 If the number of ties is moderate there will be very little difference between Equations 3 and 5, so the simpler Equation 5 may be preferred. Null Distribution The exact distribution of T is given by Table A8 for k = 3 and all ni s 5, but in general the exact distribution is too cumbersome to work with. Therefore the chi-squared distribution with k - 1 degrees of freedom is used as an approximation to the null distribution of T.

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Expert Answer

Step 1

It is given that the equations (3) and (5) are defined as

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N (N+1) 1 Т- ...-3) 4 п, 12 ) -- 3(N 1. п, T = N(N+1)

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Step 2

Consider the equation (3),

The test statistic T is defined as

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Image Transcriptionclose

- R N(N+1) n T = 4 Where, N(N+1)* 1 Σ (Χ). N-1 all 4 ranks

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Step 3

It is given that if there are no ties in th...

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N(N 1) 12

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