Question

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 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.

*H _{o}*:

*H _{o}*:

*H _{o}*:

*H _{o}*:

(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. (Use 4
decimal places.)

(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 *?* = 0.05, we do not reject
*H*_{0}.

Since the *P* value is less than or equal to the level of
significance at *?* = 0.05, we reject
*H*_{0}.

Since the *P* value is greater than the level of
significance at *?* = 0.05, we reject
*H*_{0}.

Since the *P* value is less than or equal to the level of
significance at *?* = 0.05, we do not reject
*H*_{0}.

(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.

(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 | Do not reject H0/Reject H0. | |||||

Within groups | ||||||

Total |

Answer #1

a) The null and alternate hypotheses are

against H_{1} : Not all the means are equal.

b) SSTOT = 2766.7, SSBET = 2264.8, SSW = 501.9

dfBET = 3, dfW = 17

MSBET = 167.3, MSW = 133.2

The value of the sample F statistic = 1.26

The degrees of freedom = (3, 17)

c) The P-value of the sample test statistic = 0.321

d) Since the P value is greater than the level of significance
at
= 0.05, we do not reject H_{0}.

e) At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.

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
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 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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