Question

Wild irises are beautiful flowers found throughout the United
States, Canada, and northern Europe. This problem concerns the
length of the sepal (leaf-like part covering the flower) of
different species of wild iris. Data are based on information taken
from an article by R. A. Fisher in *Annals of Eugenics*
(Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in
centimeters from random samples of *Iris setosa* (I),
*Iris versicolor* (II), and *Iris virginica* (III)
are as follows below.

I |
II |
III |

5.7 | 5.1 | 6.9 |

4.2 | 6.5 | 5.5 |

4.6 | 6.6 | 4.7 |

5.2 | 4.6 | 7.8 |

4.4 | 5.3 | 5.2 |

5.4 | 6.3 | 6.6 |

5.5 | 5.9 | |

6.3 |

Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? 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 2 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 the following--- Do not reject H0. -- Reject H0. | ||||

Within groups | ||||||

Total |

Answer #1

a)

level of significance =0.05

*H _{o}*: μ

b)

SSTOT | 17.327 |

SSBET | 4.503 |

SSW | 12.823 |

dfBET | 2 |

dfW | 18 |

MSBET | 2.2517 |

MSW | 0.7124 |

value of test statistic for factor A = | 3.16 |

df(numerator) = | 2 | |

df(Denominator) = | 18 |

c)

p value =0.0666

d)

fail to reject the null hypothesis

e) can not conclude that population means differs

f)

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

Between | 4.503 | 2 | 2.2517 | 3.16 | 0.0666 |

Within | 12.823 | 18 | 0.7124 | ||

Total | 17.327 | 20 |

do not reject ho

Wild irises are beautiful flowers found throughout the United
States, Canada, and northern Europe. This problem concerns the
length of the sepal (leaf-like part covering the flower) of
different species of wild iris. Data are based on information taken
from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part
2, pp. 179 -188). Measurements of sepal length in centimeters from
random samples of Iris setosa (I), Iris versicolor (II), and Iris
virginica (III) are as follows...

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