A botanist measures the sepal widths (in cm) of 150 iris flowers, 50 of type iri

Question

A botanist measures the sepal widths (in cm) of 150 iris flowers, 50 of type iris setosa, 50 of type iris virginica, and 50 of type iris versicolor. The data is noted below. Of interest is whether sepal width differs, on average, among the three iris types. You may assume that, for each iris type, the sample may be treated as a simple random sample.

a. What are the null and alternative hypotheses?

b. What is the value of the test statistic?

c. What is the approximate p-value?

d. State and verify (using plots or descriptive statistics) the additional two assumptions required for the p-value in c) to be valid.

e.

Sepal Width   Class
3.5 Iris-setosa
3 Iris-setosa
3.2 Iris-setosa
3.1 Iris-setosa
3.6 Iris-setosa
3.9 Iris-setosa
3.4 Iris-setosa
3.4 Iris-setosa
2.9 Iris-setosa
3.1 Iris-setosa
3.7 Iris-setosa
3.4 Iris-setosa
3 Iris-setosa
3 Iris-setosa
4 Iris-setosa
4.4 Iris-setosa
3.9 Iris-setosa
3.5 Iris-setosa
3.8 Iris-setosa
3.8 Iris-setosa
3.4 Iris-setosa
3.7 Iris-setosa
3.6 Iris-setosa
3.3 Iris-setosa
3.4 Iris-setosa
3 Iris-setosa
3.4 Iris-setosa
3.5 Iris-setosa
3.4 Iris-setosa
3.2 Iris-setosa
3.1 Iris-setosa
3.4 Iris-setosa
4.1 Iris-setosa
4.2 Iris-setosa
3.1 Iris-setosa
3.2 Iris-setosa
3.5 Iris-setosa
3.1 Iris-setosa
3 Iris-setosa
3.4 Iris-setosa
3.5 Iris-setosa
2.3 Iris-setosa
3.2 Iris-setosa
3.5 Iris-setosa
3.8 Iris-setosa
3 Iris-setosa
3.8 Iris-setosa
3.2 Iris-setosa
3.7 Iris-setosa
3.3 Iris-setosa
3.2 Iris-versicolor
3.2 Iris-versicolor
3.1 Iris-versicolor
2.3 Iris-versicolor
2.8 Iris-versicolor
2.8 Iris-versicolor
3.3 Iris-versicolor
2.4 Iris-versicolor
2.9 Iris-versicolor
2.7 Iris-versicolor
2 Iris-versicolor
3 Iris-versicolor
2.2 Iris-versicolor
2.9 Iris-versicolor
2.9 Iris-versicolor
3.1 Iris-versicolor
3 Iris-versicolor
2.7 Iris-versicolor
2.2 Iris-versicolor
2.5 Iris-versicolor
3.2 Iris-versicolor
2.8 Iris-versicolor
2.5 Iris-versicolor
2.8 Iris-versicolor
2.9 Iris-versicolor
3 Iris-versicolor
2.8 Iris-versicolor
3 Iris-versicolor
2.9 Iris-versicolor
2.6 Iris-versicolor
2.4 Iris-versicolor
2.4 Iris-versicolor
2.7 Iris-versicolor
2.7 Iris-versicolor
3 Iris-versicolor
3.4 Iris-versicolor
3.1 Iris-versicolor
2.3 Iris-versicolor
3 Iris-versicolor
2.5 Iris-versicolor
2.6 Iris-versicolor
3 Iris-versicolor
2.6 Iris-versicolor
2.3 Iris-versicolor
2.7 Iris-versicolor
3 Iris-versicolor
2.9 Iris-versicolor
2.9 Iris-versicolor
2.5 Iris-versicolor
2.8 Iris-versicolor
3.3 Iris-virginica
2.7 Iris-virginica
3 Iris-virginica
2.9 Iris-virginica
3 Iris-virginica
3 Iris-virginica
2.5 Iris-virginica
2.9 Iris-virginica
2.5 Iris-virginica
3.6 Iris-virginica
3.2 Iris-virginica
2.7 Iris-virginica
3 Iris-virginica
2.5 Iris-virginica
2.8 Iris-virginica
3.2 Iris-virginica
3 Iris-virginica
3.8 Iris-virginica
2.6 Iris-virginica
2.2 Iris-virginica
3.2 Iris-virginica
2.8 Iris-virginica
2.8 Iris-virginica
2.7 Iris-virginica
3.3 Iris-virginica
3.2 Iris-virginica
2.8 Iris-virginica
3 Iris-virginica
2.8 Iris-virginica
3 Iris-virginica
2.8 Iris-virginica
3.8 Iris-virginica
2.8 Iris-virginica
2.8 Iris-virginica
2.6 Iris-virginica
3 Iris-virginica
3.4 Iris-virginica
3.1 Iris-virginica
3 Iris-virginica
3.1 Iris-virginica
3.1 Iris-virginica
3.1 Iris-virginica
2.7 Iris-virginica
3.2 Iris-virginica
3.3 Iris-virginica
3 Iris-virginica
2.5 Iris-virginica
3 Iris-virginica
3.4 Iris-virginica
3 Iris-virginica

Using a significance level of = 0.05, state your conclusions in the language of the problem.

Explanation / Answer

#a)
data=iris
data
data.frame(data)
names(data)
sapply(data, class)
#b)
v=subset(data,Species =="setosa")
s=v$Sepal.Width
med=median(s)
med

#c)
v1=subset(data,Species =="virginica")
s1=v1$Petal.Width
ava=mean(s1)
ava

#d)
v2=subset(data,Sepal.Length>4.5,Sepal.Length<6)
vari=var(v2$Sepal.Length)
vari

#e)
rbind(v,v2)
nrow(rbind(v,v2))
#or
dim(rbind(v,v2))

unique(rbind(v,v2))
nrow(unique(rbind(v,v2)))
#or

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