Question

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 |
Sagebrush Grassland |
Pinon Juniper |

34 | 15 | 1 |

31 | 58 | 7 |

24 | 15 | 10 |

25 | 26 | 13 |

Shall we reject or accept the claim that there is no difference in the mean number of deer per square kilometer in these different ecological locations? Use a 5% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

*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.

*P*-value > 0.1000.050 < *P*-value <
0.100 0.025 < *P*-value <
0.0500.010 < *P*-value < 0.0250.001 <
*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
*H*_{0}.Since the *P*-value is less than or
equal to the level of significance at *α* = 0.05, we reject
*H*_{0}. Since the
*P*-value is greater than the level of significance at
*α* = 0.05, we reject *H*_{0}.Since the
*P*-value is less than or equal to the level of significance
at *α* = 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 not 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 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 | ---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--- Do not reject H0. Reject H0. | ||||

Within groups | ||||||

Total |

Answer #1

a) level of significance =0.05

*H _{o}*:

b)APplying ANOVA on above data:

SSTOT | 2536.917 | |||

SSBET | 1148.167 | |||

SSW | 1388.750 | |||

dfBET | 2 | |||

dfW | 9 | |||

MSBET | 574.083 | |||

MSW | 154.306 | |||

value of test statistic for factor A = | 3.720 | |||

df(numerator) = | 2 | |||

df(Denominator) = | 9 |

c)

0.050 < *P*-value < 0.10

d)Since the *P*-value is greater than the level of
significance at *α* = 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.

f)

Source of Variation |
SS |
df |
MS |
F |
P-value |
Decision |

Between Groups | 1148.167 | 2 | 574.083 | 3.720 | 0.05< p<0.10 | fail to reject Ho |

Within Groups | 1388.750 | 9 | 154.306 | |||

Total | 2536.917 | 11 |

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
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
in the mean number of deer per square kilometer in these different
ecological locations? Use a...

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
Sagebrush Grassland
Pinon Juniper
30
20
5
26
63
4
25
22
1
32
22
8
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