The data shown to the right are from independent simple random samples from three populations. Use these data to complete parts (a) through (d). Sample 1| Sample 2| Sample E Click the icon to view a table of values of F. 5 6 14 a. Compute SST, SSTR, and SSE using the following computing formulas, where x, is the ith observation, n is the total number of observations, n, is the sample size for population j, and T, is the sum of the sample data from population j. SST Σ- (Σx)*/n. SSTR - Σ (T;/n) - (ΣΧ) /n. ad SSE = SST - SSTR Compute the values required to find SST, SSTR. and SSE. n3D Ex = (Type integers or decimals. Do not round.) Calculate SST, STR, and SSE using the computing formulas.
The data shown to the right are from independent simple random samples from three populations. Use these data to complete parts (a) through (d). Sample 1| Sample 2| Sample E Click the icon to view a table of values of F. 5 6 14 a. Compute SST, SSTR, and SSE using the following computing formulas, where x, is the ith observation, n is the total number of observations, n, is the sample size for population j, and T, is the sum of the sample data from population j. SST Σ- (Σx)*/n. SSTR - Σ (T;/n) - (ΣΧ) /n. ad SSE = SST - SSTR Compute the values required to find SST, SSTR. and SSE. n3D Ex = (Type integers or decimals. Do not round.) Calculate SST, STR, and SSE using the computing formulas.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Values of Fa
dfn
4 5 6 7 8
dfd
2 3
9.
0.10
39.86
49.50
53.59
55.83
57.24
58.20
58.91
59.44
59.86
0.05
161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54
1 0.025
647.79 799.50 864.16 899.58 921.85 937.1l 948.22 956.66 963.28
0.01
4052.2 4999.5 5403.4 5624.6 5763.6 5859.0 5928.4 5981.1 6022.5
0.005
16211
20000 21615 22500 23056 23437 23715 23925 24091
0.10
8.53
9.00
9.16
9.24
9.29
9.33
9.35
9.37
9.38
0.05
18.51
19.00
19.16
19.25
19.30
19.33
19.35
19.37
19.38
2 0.025
0.01
0.005
38.51
39.00
39.17
39.25
39.30
39.33
39.36
39.37
39.39
98.50
99.00
99.17
99.25
99.30
99.33
99.36
99.37
99.39
198.50 199.00 199.17 199.25 199.30 199.33 199.36 199.37 199.39
0.10
5.54
5.46
5.39
5.34
5.31
5.28
5.27
5.25
5.24
0.05
10.13
9.55
9.28
9.12
9.01
8.94
8.89
8.85
8.81
3 0.025
17.44
16.04
15.44
15. 10
14.88
14.73
14.62
14.54
14.47
0.01
34.12
30.82
29.46
28.71
28.24
27.91
27.67
27.49
27.35
0.005
55.55
49.80
47.47
46. 19
45.39
44.84
44.43
44.13
43.88
0.10
4.54
4.32
4.19
4.11
4.05
4.01
3.98
3.95
3.94
0.05
7.71
6.94
6.59
6.39
6.26
6.16
6.09
6.04
6.00
4 0.025
12.22
10.65
9.98
9.60
9.36
9.20
9.07
8.98
8.90
0.01
21.20
18.00
16.69
15.98
15.52
15.21
14.98
14.80
14.66
0.005
31.33
26.28
24.26
23.15
22.46
21.97
21.62
21.35
21.14
0.10
4.06
3.78
3.62
3.52
3.45
3.40
3.37
3.34
3.32
5. 19
7.39
0.05
6.61
5.79
5.41
5.05
4.95
4.88
4.82
4.77
5 0.025
10.01
8.43
7.76
7.15
6.98
6.85
6.76
6.68
0.01
16.26
13.27
12.06
11.39
10.97
10.67
10.46
10.29
10.16
0.005
22.78
18.31
16.53
15.56
14.94
14.51
14.20
13.96
13.77
0.10
3.78
3.46
3.29
3.18
3.11
3.05
3.01
2.98
2.96
0.05
5.99
5.14
4.76
4.53
4.39
4.28
4.21
4.15
4.10
6 0.025
8.81
7.26
6.60
6.23
5.99
5.82
5.70
5.60
5.52
0.01
13.75
10.92
9.78
9.15
8.75
8,47
8.26
8.10
7.98
0.005
18.63
14.54
12.92
12.03
I1.46
11.07
10.79
10.57
10.39
0.10
3.59
3.26
3.07
2.96
2.88
2.83
2.78
2.75
2.72
3.68
0.05
5.59
4.74
4.35
4. 12
3.97
3.87
3.79
3.73
7 0.025
8.07
6.54
5.89
5.52
5.29
5.12
4.99
4.90
4.82
9.55
12.40
0.01
12.25
8.45
7.85
7.46
7.19
6.99
6.84
6.72
0.005
16.24
10.88
10.05
9.52
9.16
8.89
8.68
8.51
0.10
3.46
3.11
2.92
281
2.73
2.67
2.62
2.59
2.56
0.05
5.32
4.46
4.07
3.84
3.69
3.58
3.50
3.44
3.39
8 0.025
0.01
7.57
6.06
5.42
5.05
4.82
4.65
4.53
4.43
4.36
11.26
8.65
7.59
7.01
6.63
6.37
6. 18
6.03
5.91
0.005
14.69
11.04
9.60
8.81
8.30
7.95
7.69
7.50
7.34
Transcribed Image Text:TITT
The data shown to the right are from independent simple random samples from three populations. Use these data to complete parts (a) through (d).
Sample 1| Sample 2| Sample 3 o
3
5
Click the icon to view a table of values of Fa.
6
2
14
a. Compute SST, SSTR, and SSE using the following computing formulas, where x, is the ith observation, n is the total number of observations, n; is the sample size for population j, and T; is the sum of the sample data from population j.
SST = Ex? - (Ex)² /n, SSTR = E (T? /n) - (Ex)² /n, and sSE = SST -SSTR
Compute the values required to find SST, SSTR, and SSE.
n=
Ex =
Ex? =
E(1; /n) =
(Type integers or decimals. Do not round.)
Calculate SST, SSTR, and SSE using the computing formulas.
SST =
(Type an integer or a decimal. Do not round.)
SSTR=
(Type an integer or a decimal. Do not round.)
SSE =
(Type an integer or a decimal. Do not round.)
b. Compare your results in part (a) for SSTR and SSE with the following results from the defining formulas.
SSTR Ση (-)
and SSE = E(n - 1)s =
the same value as when it is found by using the computing formula. When the value of SSE is found by using the defining formula, it
When the value of SSTR is found by using the defining formula, it
value as when it is found by using the computing formula.
the same
c. Construct a one-way ANOVA table.
Source
df
MS
F-statistic
Treatment
Error
Total
(Type integers or decimals rounded to two decimal places as needed.)
d. Decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that the means of the populations from which the samples were drawn are not all the same.
First, let u,, Hz, and pa be the population means of samples 1, 2, and 3, respectively. What are the correct hypotheses for a one-way ANOVA test?
OA. Ho: H1 =2 = H3
O B. Hg: H1 =H2 =H3
H: Not all the means are equal.
O C. Ho: H1 #µ2 #H3
H: All the means are equal.
O D. H,: H, H2 #H3
H H =2 =H3
Now determine the critical value F
Fa =
(Round to two decimal places as needed.)
Finally, what is the correct conclusion?
Since the F-statistic
in the rejection region,
Ho- The data
sufficient evidence to conclude that the population means are not all the same.
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