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 |

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 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 (from the following).

*H _{o}*: μ

*H _{o}*: μ

*H _{o}*: μ

*H _{o}*: μ

(b) Find *SS _{TOT}, SS_{BET}*, and

SS_{TOT} |
= | |

SS_{BET} |
= | |

SS_{W} |
= |

Find *d.f. _{BET}, d.f._{W},
MS_{BET}*, and

df_{BET} |
= | |

df_{W} |
= | |

MS_{BET} |
= | |

MS_{W} |
= |

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.

(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis?

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

(f) Make a summary table for your ANOVA test.

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

Between groups | ---Select from the following--- 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 from following--- Do not reject H0. -- Reject H0. | ||||

Within groups | ||||||

Total |

Answer #1

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

a)level of significance=0.05

*H _{o}*: μ

b)

SSTOT | 2362.286 |

SSBET | 399.252 |

SSW | 1963.033 |

dfBET | 3 |

dfW | 17 |

MSBET | 133.084 |

MSW | 115.473 |

value of test statistic for factor A = | 1.153 |

df(numerator) = | 3 | |

df(Denominator) = | 17 |

c)

p value = 0.3566

d) fail to reject the null hypothesis

e) can not conclude that means are different

f)

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

Between | 399.252 | 3 | 133.084 | 1.153 | 0.3566 |

Within | 1963.033 | 17 | 115.473 | ||

Total | 2362.286 | 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 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...

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
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Site I
Site II
Site III
Site IV
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17
39
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29
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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
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13
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