For Part II of the lab, we will focus on the Versicolor species. In particular,

Question

For Part II of the lab, we will focus on the Versicolor species. In particular, we are interested in the mean difference between sepal length and sepal width. Biologists claim that the difference between length and width (length – width) is 3 cm. We would like to assess if this claim is reasonable given our data. Assume that the population standard deviations for both sepal length and sepal width are 0.5. Since each flower is being measured twice, this is a matched pairs data set.

R Code:

versicolor_sepal <- iris %>% filter(Species == "versicolor") %>% select(Sepal.Length, Sepal.Width)

Are 50 samples of versicolor enough to detect an alternative mean difference of 3.1? Why or why not?

A observed Sampl Mean = 3.166 Critical Region for alpha = 5% critical values = 2.8777, 3.1223 2.8 2.9 3.0 3.1 3.2 Difference of Sample Means

Explanation / Answer

Since given sample mean lies within the critical region which is indicated by red color .

We reject null hypothesis Ho i.e mean difference is 3. At 5% significance level.

It means we have sufficient evidence to conclude that the alternative mean difference is of 3.1

Means 50 samples are enough to detect an alternative mean difference is 3.1.

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