Question

Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four different sites in an archaeological region, the number of such sherds was counted in local dwelling excavations. Site I Site II Site III Site IV 15 12 33 11 29 5 23 19 7 33 14 10 22 2 47 38 16 27 15 13 16 Shall we reject or not reject the claim that there is no difference in the population mean three-circle red-on-white sherd counts for the four sites? Use a 5% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly three means are equal. Ho: μ1 = μ2 = μ3 = μ4; H1: All four means are different. Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly two means are equal. Ho: μ1 = μ2 = μ3 = μ4; H1: Not all the means are equal. Correct: Your answer is correct. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.) dfBET = dfW = MSBET = MSW = Find the value of the sample F statistic. (Use 3 decimal places.) What are the degrees of freedom? (numerator) (denominator) (c) Find the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.001 < P-value < 0.010 P-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value is greater than the level of significance at α = 0.05, we do not reject H0. Since the P-value is less than or equal to the level of significance at α = 0.05, we reject H0. Since the P-value is greater than the level of significance at α = 0.05, we reject H0. Since the P-value is less than or equal to the level of significance at α = 0.05, we do not reject H0. Correct: Your answer is correct. (e) Interpret your conclusion in the context of the application. At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal. At the 5% level of significance there is sufficient evidence to conclude that the means are all equal. At the 5% level of significance there is insufficient evidence to conclude that the means are all equal. At the 5% level of significance there is sufficient evidence to conclude that the means are not all equal. Correct: Your answer is correct. (f) Make a summary table for your ANOVA test. Source of Variation Sum of Squares Degrees of Freedom MS F Ratio P Value Test Decision Between groups Within groups Total

Answer #1

The data is considered as 6 values for site 1 and 5 for 2,3 and 4

A)Level of significance =0.05

Null and alternative hypothesis : Ho: μ1 = μ2 = μ3 = μ4; H1: Not all the means are equal.

B)SSTOT=2656.952

SSBET=338.652

SSW=2318.300

We get SSTOT = SSBET+ SSW

df BET=3

df W=17

MSBET=112.884

MSW=136.371

F= 0.828

Degrees of freedom =(3, 17)

C)P value is .497 > .1

D)The conclusion on Ho is Since the P-value is greater than the level of significance at α = 0.05, we do not reject H0.

E) Interpretation: At the 5% level of significance there is sufficient evidence to conclude that the means are all equal

F)ANOVA Table

Source | SS | df | MS | F | p value | Decision |
---|---|---|---|---|---|---|

Between | 338.652 | 3 | 112.884 | 0.828 | 0.497 | Accept |

Within | 2318.3 | 17 | 136.371 | |||

Total | 2656.952 | 20 |

Another type of painted ceramic vessel is called
three-circle red-on-white ( Mimbres Mogollon
Archaeology). At four different sites in an archaeological
region, the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
Site IV
18
11
37
17
28
4
19
23
9
35
11
17
22
3
45
36
10
29
19
11
11
Shall we reject or not reject the claim that there is no
difference in the population mean three-circle...

Another type of painted ceramic vessel is called
three-circle red-on-white ( Mimbres Mogollon
Archaeology). At four different sites in an archaeological
region, the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
Site IV
19
15
38
13
22
8
15
17
5
30
10
16
22
8
47
37
10
24
19
12
18
Shall we reject or not reject the claim that there is no
difference in the population mean three-circle...

Another type of painted ceramic vessel is called
three-circle red-on-white ( Mimbres Mogollon
Archaeology). At four different sites in the Wind Mountain
archaeological region, the number of such sherds was counted in
local dwelling excavations.
Site I
Site II
Site III
Site IV
14
17
39
10
29
3
17
22
4
35
12
15
20
6
49
31
11
24
13
18
17
Shall we reject or not reject the claim that there is no
difference in the population...

Another type of painted ceramic vessel is called
three-circle red-on-white ( Mimbres Mogollon
Archaeology). At four different sites in an archaeological
region, the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
Site IV
19
12
38
15
27
5
20
17
7
35
16
12
19
3
44
35
17
22
15
17
13
Shall we reject or not reject the claim that there is no
difference in the population mean three-circle...

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The deer counts per square kilometer were recorded and are shown in
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29
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10
27
59
3
25
16
2
27
24
6
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A random sample of companies in electric utilities (I),
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following information regarding annual profits per employee (units
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II
III
49.7
55.8
38.9
43.3
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37.7
32.9
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10.7
27.4
29.2
32.6
38.3
39.6
15.2
36.8
42.5
20.1
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of the three types of companies? Use...

Where are the deer? Random samples of square-kilometer plots
were taken in different ecological locations of a national park.
The deer counts per square kilometer were recorded and are shown in
the following table.
Mountain Brush
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34
15
1
31
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24
15
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25
26
13
Shall we reject or accept the claim that there is no difference
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49.3
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37.3
32.6
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