Question

In: Statistics and Probability

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

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.

Solutions

Expert Solution

a)
ho: there is no significant difference in the mean sepal between three types of iris.
h1: at least one of the mean sepal between three types of iris differ significantly.

b)

F test statistic = 47.36

c)
p-value = 0.000

d)
With F=47.36, p<5%, I reject ho and conclude that at least one of the mean sepal between three types of iris differ significantly.

The same is observed from the interval plot. the sepal width for iris Sentosa is the highest as compared to versi-color and virginica.

assumption 1:

Ho: there is equality of variances between three types of iris. V/s h1: there is in-equality of variances between three types of iris. With Levenes, W=0.65, p>5%, I fail to reject ho and conclude that there is equality of variances between three types of iris.

assumption 2:

There are no outliers in the data set.

procedure 1:

stat -> ANOVA -> one way
response -> sepal width
factor -> class
ok

output 1:

Procedure 2:

stat -> ANOVA -> test with equal variances
response -> sepal width
factor -> class
ok

Output 2:

orchestra answered 2 years ago
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