Question

There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
*Mimbres classic black-on-white*. At three different sites,
the number of such sherds was counted in local dwelling
excavations.

Site I |
Site II |
Site III |

65 | 21 | 17 |

30 | 19 | 35 |

23 | 53 | 71 |

17 | 68 | 24 |

76 | 12 | |

52 | 17 | |

21 |

Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3};
*H*_{1}: Not all the means are equal.

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3};
*H*_{1}: At least two means are
equal.

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3};
*H*_{1}: Exactly two means are equal.

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3};
*H*_{1}: All three means are different.

(b) Find *SS*_{TOT},
*SS*_{BET}, and
*SS*_{W} and check that
*SS*_{TOT} =
*SS*_{BET} +
*SS*_{W}. (Round your answers to three
decimal places.)

SS_{TOT} |
= | |

SS_{BET} |
= | |

SS_{W} |
= |

Find *d.f.*_{BET},
*d.f.*_{W},
*MS*_{BET}, and
*MS*_{W}. (Round your answers for
*MS _{BET}*, and

d.f._{BET} |
= | |

d.f._{W} |
= | |

MS_{BET} |
= | |

MS_{W} |
= |

Find the value of the sample *F* statistic. (Round your
answer to two decimal places.)

What are the degrees of freedom?

d.f._{N} |
= |

d.f._{D} |
= |

(c) Find the *P*-value of the sample test statistic. Select
one

*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* = 0.01, we do not reject
*H*_{0}.

Since the *P*-value is less than or equal to the level of
significance at *α* = 0.01, we reject
*H*_{0}.

Since the *P*-value is greater than the level of
significance at *α* = 0.01, we reject
*H*_{0}.

Since the *P*-value is less than or equal to the level of
significance at *α* = 0.01, we do not reject
*H*_{0}.

(e) Interpret your conclusion in the context of the application.
Select one

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.

At the 1% level of significance there is sufficient evidence to conclude that the means are all equal.

At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.

At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal.

(f) Make a summary table for your ANOVA test. (Round your answers
for SS to three decimal places, your MS and *F* Ratio to two
decimal places, and your *P*-value to four decimal
places.)

Source of Variation |
Sum of Squares |
Degrees of Freedom |
MS | FRatio |
P-Value |
Test Decision |

Between groups | ---Select--- 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 | ---Select--- Reject H0. Do not reject H0. | ||||

Within groups | ||||||

Total |

Answer #1

Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array): |

a)the level of significance =0.01

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3};
*H*_{1}: Not all the means are equal.

b)

SSTOT | 7978.235 |

SSBET | 480.438 |

SSW | 7497.798 |

dfBET | 2 |

dfW | 14 |

MSBET | 240.22 |

MSW | 535.56 |

value of test statistic for factor A = | 0.45 |

df(numerator) = | 2 | |

df(Denominator) = | 14 |

c)

*P*-value > 0.100

d)

Since the *P*-value is greater than the level of
significance at *α* = 0.01, we do not reject
*H*_{0}.

e)

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.

f)

Source | SS | df | MS | F | P value |

Between | 480.438 | 2 | 240.22 | 0.45 | 0.6474 |

Within | 7497.798 | 14 | 535.56 | do not reject Ho | |

Total | 7978.235 | 16 |

There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
Mimbres classic black-on-white. At three different sites,
the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
62
29
17
39
18
34
27
54
74
17
60
28
81
18
52
12
23
Shall we reject or not reject the claim that there...

There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
Mimbres classic black-on-white. At three different sites,
the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
64
26
15
35
17
32
22
54
65
11
68
28
77
16
54
13
20
Shall we reject or not reject the claim that there...

There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
Mimbres classic black-on-white. At three different sites,
the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
64
24
18
33
14
30
22
50
73
17
61
29
82
14
56
16
26
Shall we reject or not reject the claim that there...

There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
Mimbres classic black-on-white. At three different sites,
the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
65
20
10
30
15
33
23
57
71
15
60
23
77
13
50
18
29
Shall we reject or not reject the claim that there...

There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
Mimbres classic black-on-white. At three different sites, the
number of such sherds was counted in local dwelling
excavations.
Site I (67,35,28,17,82,50,26)
Site Il (28.18,54, 69)
Site III (13,35, 74, 24, 15, 11)
(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET +
SSW. (Round your answers to three...

#13
There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
Mimbres classic black-on-white. At three different sites,
the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
64
26
17
39
10
38
24
58
72
11
62
22
81
18
52
13
28
(b) Find SSTOT,
SSBET, and
SSW and check that...

There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
Mimbres classic black-on-white. At three different sites,
the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
69
26
15
39
16
31
29
50
72
10
63
29
80
10
57
17
29
Shall we reject or not reject the claim that there...

Where are the deer? Random samples of square-kilometer plots
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The deer counts per square kilometer were recorded and are shown in
the following table.
Mountain Brush
Sagebrush Grassland
Pinon Juniper
29
24
10
27
59
3
25
16
2
27
24
6
Shall we reject or accept the claim that there is no difference
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A random sample of companies in electric utilities (I),
financial services (II), and food processing (III) gave the
following information regarding annual profits per employee (units
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I
II
III
49.7
55.8
38.9
43.3
25.3
37.7
32.9
41.7
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
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of the three types of companies? Use...

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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I
II
III
49.3
55.7
38.7
43.3
25.0
37.3
32.6
41.5
10.9
27.1
29.4
32.9
38.5
39.9
15.5
36.5
42.2
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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...

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