STEP 1: State the hypotheses and select an alpha level.H0: µ1 = µ2 = µ3 (There is no treatment effect.)H1: At least one of the treatment means is different.We use α = .05STEP 2: Locate the critical region.df total = N - 1 =df between = k - 1 = (Numerator)df within = N – k = (Denominator)look up in the f table: df = Numerator, Denominator, Critical region =STEP 3: Compute the F-ratio.SS total = ΣX^2-G^2/N =SS within = ΣSS inside each treatment =SSbetween = SStotal – SSwithin = Calculation of mean squaresMS between=(SS between)/(ⅆf between)MS within=(SS within)/(ⅆf within)Calculation of F.F=(MS between)/(MS within)= STEP 4 : MAKE A DECISION The following data were obtained from an indepen-dent-measures research study comparing three treat-ment conditions. Use an ANOVA with a = .05to determine whether there are any significant meandifferences among the treatments.TreatmentIIn = 8n = 6n = 4N = 18T = 16T = 24T = 32G = 72SS = 40SS = 24SS = 16EX = 464%3D The F Distribution**Table entries in lightface type are critical values for the 05 level of significance.Boldface type values are for the .01 level of significance.CriticałDegrees ofFreedom:DenominatorDegrees of Freedom: Numerator3.478910111214162012392004999 5403 562521623057641612252342372412422432442466106 6142 6169 6208245248405258595928598160226056608219.3619.3719.3819.41 19.42 19.43 19.4499.42 99.43 99.44 99.45218.51 19.00 19.16 19.25 19.30 19.3319.3919.4098.49 99.00 99.17 99.25 99.30 99.3399.3499.36 99.3899.40 99.418.8828.24 27.91 27.678.948.848.818.69 8.6627.23 27.13 27.05 26.92 26.83 26.6910.13 9.55 9.289.129.018.788.768.748.713.34.12 30.92 29.46 28.7127.49 27.346.045.9614.54 14.45 14.37 14.24 14.15 14.026.946.596.396.266.166.096.005.915.877.7121.20 18.00 16.69 15.9845.935.845.8015.52 15.21 14.9814.80 14.666.615.795.195.054.954.884.824.784.744.701.681.611.60 1.569.6855.4116.26 13.27 12.06 11.39 10.97 10.67 10.4510.27 10.1510.059.969.899.779.554.158.105.14 4.764.534.104.064.398.754.007.7265.994.284.214.033.963.92 3.8713.74 10.92 9.789.158.478.267.987.877.797.607.527.393.793.736.844.74 4.353.973.873.683.633.605.5912.253.496.2774.123.573.523.449.55 8.457.857.467.197.006.716.626.546.476.356.153.506.193.285.674.46 4.073.693.586.373.395.913.343.313.235.565.323.843.443.205.483.155.36811.268.65 7.597.016.636.035.825.745.123.373.233.29.5.623.183.133.103.075.114.26 3.863.023.636.429.3.482.982.9310.568.02 6.996.065.805.475.355.265.185.004.924.803.075.062.973.024.952.914.712.944.9610.043.483.335.643.223.145.212.864.604.10 3.712.824.52102.777.56 6.555.995.394.854.784.413.095.072.952.904.849.653.596.223.205.322.824.46I 13.983.363.012.862.792.742.70 2.657.205.674.884.744.634.544.404.294,214.103.265.413.004.822.804.392.764.303.492.693.115.062.922.854.502.724.222.642.60 2.544.759.333.886.93 5.95124.654.164.053.983.862.674.102.633.024.862.922.842.772.722.604.679.073.806.70 5.742.553.853.182.513.78133.412.465.204.624.444.304.194.023.963.672.852.654.03144.603.743.343.112.962.772.702.602.562.532.482.442.398.866.515.565.034.694.464.284.143.943.863.803.703.62 3.512.792.592.552.704.142.642.482.432.393.56 3.482.902.512.334.548.68153.683.293.066.365.424.894.564.324.003.893.803.733.673.362.662.593.892.542.8.54.442.742.492.452.422.372.283.37 3.25164.493.633.243.012.338.536.235.294.774.204.033.783.693.613.553.45

Name: STEP 1: State the hypotheses and select an alpha level.H0: µ1 = µ2 = µ
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Description: STEP 1: State the hypotheses and select an alpha level.H0: µ1 = µ2 = µ3 (There is no treatment effect.)H1: At least one of the treatment means is different.We use α = .05STEP 2: Locate the critical region.df total = N - 1 =df between = k - 1 = (Numer

STEP 1: The hypothesis is, Null hypothesis: H0:μ1=μ2=μ3 Alternative hypothesis: H1: At least one of…

Answered: STEP 1: State the hypotheses and select…

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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STEP 1: State the hypotheses and select an alpha level.
H0: µ1 = µ2 = µ3 (There is no treatment effect.)
H1: At least one of the treatment means is different.
We use α = .05

STEP 2: Locate the critical region.

df total = N - 1 =

df between = k - 1 = (Numerator)

df within = N – k = (Denominator)

look up in the f table: df = Numerator, Denominator, Critical region =

STEP 3: Compute the F-ratio.

SS total = ΣX^2-G^2/N =

SS within = ΣSS inside each treatment =

SSbetween = SStotal – SSwithin
=
Calculation of mean squares
MS between=(SS between)/(ⅆf between)
MS within=(SS within)/(ⅆf within)

Calculation of F.

F=(MS between)/(MS within)
=
STEP 4 : MAKE A DECISION

The following data were obtained from an indepen-
dent-measures research study comparing three treat-
ment conditions. Use an ANOVA with a = .05
to determine whether there are any significant mean
differences among the treatments.
Treatment
II
n = 8
n = 6
n = 4
N = 18
T = 16
T = 24
T = 32
G = 72
SS = 40
SS = 24
SS = 16
EX = 464
%3D

The F Distribution*
*Table entries in lightface type are critical values for the 05 level of significance.
Boldface type values are for the .01 level of significance.
Criticał
Degrees of
Freedom:
Denominator
Degrees of Freedom: Numerator
3.
4
7
8
9
10
11
12
14
16
20
1
239
200
4999 5403 5625
216
230
5764
161
225
234
237
241
242
243
244
246
6106 6142 6169 6208
245
248
4052
5859
5928
5981
6022
6056
6082
19.36
19.37
19.38
19.41 19.42 19.43 19.44
99.42 99.43 99.44 99.45
2
18.51 19.00 19.16 19.25 19.30 19.33
19.39
19.40
98.49 99.00 99.17 99.25 99.30 99.33
99.34
99.36 99.38
99.40 99.41
8.88
28.24 27.91 27.67
8.94
8.84
8.81
8.69 8.66
27.23 27.13 27.05 26.92 26.83 26.69
10.13 9.55 9.28
9.12
9.01
8.78
8.76
8.74
8.71
3.
34.12 30.92 29.46 28.71
27.49 27.34
6.04
5.96
14.54 14.45 14.37 14.24 14.15 14.02
6.94
6.59
6.39
6.26
6.16
6.09
6.00
5.91
5.87
7.71
21.20 18.00 16.69 15.98
4
5.93
5.84
5.80
15.52 15.21 14.98
14.80 14.66
6.61
5.79
5.19
5.05
4.95
4.88
4.82
4.78
4.74
4.70
1.68
1.61
1.60 1.56
9.68
5
5.41
16.26 13.27 12.06 11.39 10.97 10.67 10.45
10.27 10.15
10.05
9.96
9.89
9.77
9.55
4.15
8.10
5.14 4.76
4.53
4.10
4.06
4.39
8.75
4.00
7.72
6
5.99
4.28
4.21
4.03
3.96
3.92 3.87
13.74 10.92 9.78
9.15
8.47
8.26
7.98
7.87
7.79
7.60
7.52
7.39
3.79
3.73
6.84
4.74 4.35
3.97
3.87
3.68
3.63
3.60
5.59
12.25
3.49
6.27
7
4.12
3.57
3.52
3.44
9.55 8.45
7.85
7.46
7.19
7.00
6.71
6.62
6.54
6.47
6.35
6.15
3.50
6.19
3.28
5.67
4.46 4.07
3.69
3.58
6.37
3.39
5.91
3.34
3.31
3.23
5.56
5.32
3.84
3.44
3.20
5.48
3.15
5.36
8
11.26
8.65 7.59
7.01
6.63
6.03
5.82
5.74
5.12
3.37
3.23
3.29.
5.62
3.18
3.13
3.10
3.07
5.11
4.26 3.86
3.02
3.63
6.42
9.
3.48
2.98
2.93
10.56
8.02 6.99
6.06
5.80
5.47
5.35
5.26
5.18
5.00
4.92
4.80
3.07
5.06
2.97
3.02
4.95
2.91
4.71
2.94
4.96
10.04
3.48
3.33
5.64
3.22
3.14
5.21
2.86
4.60
4.10 3.71
2.82
4.52
10
2.77
7.56 6.55
5.99
5.39
4.85
4.78
4.41
3.09
5.07
2.95
2.90
4.84
9.65
3.59
6.22
3.20
5.32
2.82
4.46
I 1
3.98
3.36
3.01
2.86
2.79
2.74
2.70 2.65
7.20
5.67
4.88
4.74
4.63
4.54
4.40
4.29
4,21
4.10
3.26
5.41
3.00
4.82
2.80
4.39
2.76
4.30
3.49
2.69
3.11
5.06
2.92
2.85
4.50
2.72
4.22
2.64
2.60 2.54
4.75
9.33
3.88
6.93 5.95
12
4.65
4.16
4.05
3.98
3.86
2.67
4.10
2.63
3.02
4.86
2.92
2.84
2.77
2.72
2.60
4.67
9.07
3.80
6.70 5.74
2.55
3.85
3.18
2.51
3.78
13
3.41
2.46
5.20
4.62
4.44
4.30
4.19
4.02
3.96
3.67
2.85
2.65
4.03
14
4.60
3.74
3.34
3.11
2.96
2.77
2.70
2.60
2.56
2.53
2.48
2.44
2.39
8.86
6.51
5.56
5.03
4.69
4.46
4.28
4.14
3.94
3.86
3.80
3.70
3.62 3.51
2.79
2.59
2.55
2.70
4.14
2.64
2.48
2.43
2.39
3.56 3.48
2.90
2.51
2.33
4.54
8.68
15
3.68
3.29
3.06
6.36
5.42
4.89
4.56
4.32
4.00
3.89
3.80
3.73
3.67
3.36
2.66
2.59
3.89
2.54
2.8.5
4.44
2.74
2.49
2.45
2.42
2.37
2.28
3.37 3.25
16
4.49
3.63
3.24
3.01
2.33
8.53
6.23
5.29
4.77
4.20
4.03
3.78
3.69
3.61
3.55
3.45

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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