Question

# Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem...

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)
Ho: μ1 = μ2 = μ3; H1: Not all the means are equal.

Ho: μ1 = μ2 = μ3; H1: All three means are different.

Ho: μ1 = μ2 = μ3; H1: Exactly two means are equal.

Ho: μ1 = μ2 = μ3; H1: At least two means are equal.

(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)

 SSTOT = SSBET = SSW =

Find d.f.BET, d.f.W, MSBET, and MSW. (Use 4 decimal places for MSBET, and MSW.)

 dfBET = dfW = MSBET = MSW =

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 F Ratio 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

a)

level of significance =0.05

Ho: μ1 = μ2 = μ3; H1: Not all the means are equal.

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

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