Test the null hypothesis that the mean sepal widths for versicolor and virginica

Question

Test the null hypothesis that the mean sepal widths for versicolor and virginica are the same against the alternative that they are different. Give a p-value.

DATASET: iris

"Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"
5.1 3.5 1.4 0.2 "setosa"
4.9 3 1.4 0.2 "setosa"
4.7 3.2 1.3 0.2 "setosa"
4.6 3.1 1.5 0.2 "setosa"
5 3.6 1.4 0.2 "setosa"
5.4 3.9 1.7 0.4 "setosa"
4.6 3.4 1.4 0.3 "setosa"
5 3.4 1.5 0.2 "setosa"
4.4 2.9 1.4 0.2 "setosa"
4.9 3.1 1.5 0.1 "setosa"
5.4 3.7 1.5 0.2 "setosa"
4.8 3.4 1.6 0.2 "setosa"
4.8 3 1.4 0.1 "setosa"
4.3 3 1.1 0.1 "setosa"
5.8 4 1.2 0.2 "setosa"
5.7 4.4 1.5 0.4 "setosa"
5.4 3.9 1.3 0.4 "setosa"
5.1 3.5 1.4 0.3 "setosa"
5.7 3.8 1.7 0.3 "setosa"
5.1 3.8 1.5 0.3 "setosa"
5.4 3.4 1.7 0.2 "setosa"
5.1 3.7 1.5 0.4 "setosa"
4.6 3.6 1 0.2 "setosa"
5.1 3.3 1.7 0.5 "setosa"
4.8 3.4 1.9 0.2 "setosa"
5 3 1.6 0.2 "setosa"
5 3.4 1.6 0.4 "setosa"
5.2 3.5 1.5 0.2 "setosa"
5.2 3.4 1.4 0.2 "setosa"
4.7 3.2 1.6 0.2 "setosa"
4.8 3.1 1.6 0.2 "setosa"
5.4 3.4 1.5 0.4 "setosa"
5.2 4.1 1.5 0.1 "setosa"
5.5 4.2 1.4 0.2 "setosa"
4.9 3.1 1.5 0.2 "setosa"
5 3.2 1.2 0.2 "setosa"
5.5 3.5 1.3 0.2 "setosa"
4.9 3.6 1.4 0.1 "setosa"
4.4 3 1.3 0.2 "setosa"
5.1 3.4 1.5 0.2 "setosa"
5 3.5 1.3 0.3 "setosa"
4.5 2.3 1.3 0.3 "setosa"
4.4 3.2 1.3 0.2 "setosa"
5 3.5 1.6 0.6 "setosa"
5.1 3.8 1.9 0.4 "setosa"
4.8 3 1.4 0.3 "setosa"
5.1 3.8 1.6 0.2 "setosa"
4.6 3.2 1.4 0.2 "setosa"
5.3 3.7 1.5 0.2 "setosa"
5 3.3 1.4 0.2 "setosa"
7 3.2 4.7 1.4 "versicolor"
6.4 3.2 4.5 1.5 "versicolor"
6.9 3.1 4.9 1.5 "versicolor"
5.5 2.3 4 1.3 "versicolor"
6.5 2.8 4.6 1.5 "versicolor"
5.7 2.8 4.5 1.3 "versicolor"
6.3 3.3 4.7 1.6 "versicolor"
4.9 2.4 3.3 1 "versicolor"
6.6 2.9 4.6 1.3 "versicolor"
5.2 2.7 3.9 1.4 "versicolor"
5 2 3.5 1 "versicolor"
5.9 3 4.2 1.5 "versicolor"
6 2.2 4 1 "versicolor"
6.1 2.9 4.7 1.4 "versicolor"
5.6 2.9 3.6 1.3 "versicolor"
6.7 3.1 4.4 1.4 "versicolor"
5.6 3 4.5 1.5 "versicolor"
5.8 2.7 4.1 1 "versicolor"
6.2 2.2 4.5 1.5 "versicolor"
5.6 2.5 3.9 1.1 "versicolor"
5.9 3.2 4.8 1.8 "versicolor"
6.1 2.8 4 1.3 "versicolor"
6.3 2.5 4.9 1.5 "versicolor"
6.1 2.8 4.7 1.2 "versicolor"
6.4 2.9 4.3 1.3 "versicolor"
6.6 3 4.4 1.4 "versicolor"
6.8 2.8 4.8 1.4 "versicolor"
6.7 3 5 1.7 "versicolor"
6 2.9 4.5 1.5 "versicolor"
5.7 2.6 3.5 1 "versicolor"
5.5 2.4 3.8 1.1 "versicolor"
5.5 2.4 3.7 1 "versicolor"
5.8 2.7 3.9 1.2 "versicolor"
6 2.7 5.1 1.6 "versicolor"
5.4 3 4.5 1.5 "versicolor"
6 3.4 4.5 1.6 "versicolor"
6.7 3.1 4.7 1.5 "versicolor"
6.3 2.3 4.4 1.3 "versicolor"
5.6 3 4.1 1.3 "versicolor"
5.5 2.5 4 1.3 "versicolor"
5.5 2.6 4.4 1.2 "versicolor"
6.1 3 4.6 1.4 "versicolor"
5.8 2.6 4 1.2 "versicolor"
5 2.3 3.3 1 "versicolor"
5.6 2.7 4.2 1.3 "versicolor"
5.7 3 4.2 1.2 "versicolor"
5.7 2.9 4.2 1.3 "versicolor"
6.2 2.9 4.3 1.3 "versicolor"
5.1 2.5 3 1.1 "versicolor"
5.7 2.8 4.1 1.3 "versicolor"
6.3 3.3 6 2.5 "virginica"
5.8 2.7 5.1 1.9 "virginica"
7.1 3 5.9 2.1 "virginica"
6.3 2.9 5.6 1.8 "virginica"
6.5 3 5.8 2.2 "virginica"
7.6 3 6.6 2.1 "virginica"
4.9 2.5 4.5 1.7 "virginica"
7.3 2.9 6.3 1.8 "virginica"
6.7 2.5 5.8 1.8 "virginica"
7.2 3.6 6.1 2.5 "virginica"
6.5 3.2 5.1 2 "virginica"
6.4 2.7 5.3 1.9 "virginica"
6.8 3 5.5 2.1 "virginica"
5.7 2.5 5 2 "virginica"
5.8 2.8 5.1 2.4 "virginica"
6.4 3.2 5.3 2.3 "virginica"
6.5 3 5.5 1.8 "virginica"
7.7 3.8 6.7 2.2 "virginica"
7.7 2.6 6.9 2.3 "virginica"
6 2.2 5 1.5 "virginica"
6.9 3.2 5.7 2.3 "virginica"
5.6 2.8 4.9 2 "virginica"
7.7 2.8 6.7 2 "virginica"
6.3 2.7 4.9 1.8 "virginica"
6.7 3.3 5.7 2.1 "virginica"
7.2 3.2 6 1.8 "virginica"
6.2 2.8 4.8 1.8 "virginica"
6.1 3 4.9 1.8 "virginica"
6.4 2.8 5.6 2.1 "virginica"
7.2 3 5.8 1.6 "virginica"
7.4 2.8 6.1 1.9 "virginica"
7.9 3.8 6.4 2 "virginica"
6.4 2.8 5.6 2.2 "virginica"
6.3 2.8 5.1 1.5 "virginica"
6.1 2.6 5.6 1.4 "virginica"
7.7 3 6.1 2.3 "virginica"
6.3 3.4 5.6 2.4 "virginica"
6.4 3.1 5.5 1.8 "virginica"
6 3 4.8 1.8 "virginica"
6.9 3.1 5.4 2.1 "virginica"
6.7 3.1 5.6 2.4 "virginica"
6.9 3.1 5.1 2.3 "virginica"
5.8 2.7 5.1 1.9 "virginica"
6.8 3.2 5.9 2.3 "virginica"
6.7 3.3 5.7 2.5 "virginica"
6.7 3 5.2 2.3 "virginica"
6.3 2.5 5 1.9 "virginica"
6.5 3 5.2 2 "virginica"
6.2 3.4 5.4 2.3 "virginica"
5.9 3 5.1 1.8 "virginica"

Explanation / Answer

Copy the data into Excel and save into .csv format.

> data1=read.csv(file.choose(),header=T) #importing the csv file into R
> attach(data1) #attaching the dataset
> names(data1)
[1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"
> Sepal.Width[Species=="virginica"]
[1] 3.3 2.7 3.0 2.9 3.0 3.0 2.5 2.9 2.5 3.6 3.2 2.7 3.0 2.5 2.8 3.2 3.0 3.8 2.6
[20] 2.2 3.2 2.8 2.8 2.7 3.3 3.2 2.8 3.0 2.8 3.0 2.8 3.8 2.8 2.8 2.6 3.0 3.4 3.1
[39] 3.0 3.1 3.1 3.1 2.7 3.2 3.3 3.0 2.5 3.0 3.4 3.0
> Sepal.Width[Species=="versicolor"]
[1] 3.2 3.2 3.1 2.3 2.8 2.8 3.3 2.4 2.9 2.7 2.0 3.0 2.2 2.9 2.9 3.1 3.0 2.7 2.2
[20] 2.5 3.2 2.8 2.5 2.8 2.9 3.0 2.8 3.0 2.9 2.6 2.4 2.4 2.7 2.7 3.0 3.4 3.1 2.3
[39] 3.0 2.5 2.6 3.0 2.6 2.3 2.7 3.0 2.9 2.9 2.5 2.8
> t.test(Sepal.Width[Species=="virginica"] ,Sepal.Width[Species=="versicolor"],alt="two.sided",paired=F) #two-sample t-test

Welch Two Sample t-test

data: Sepal.Width[Species == "virginica"] and Sepal.Width[Species == "versicolor"]
t = 3.2058, df = 97.927, p-value = 0.001819
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.07771636 0.33028364
sample estimates:
mean of x mean of y
2.974 2.770

Since p-value is < 0.05, we reject the null hypothesis of equal means of both the groups and conclude that the means of sepal width of versicolor and virginia differ significantly.

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