Chapter PVI, Problem 28RE

(a)

To determine

To make a parallel boxplots of petal lengths for the two species.

Explanation of Solution

It is given in the question that the researchers want to know that can measurements of the petal length of flowers be of value when you need to determine the species of a certain flower. Thus, the box plots for the petal lengths for the two species are as follows:

  

In this box plot the left box plot is for the species Versicolor and right box plot is for the species Virginica.

(b)

To determine

To describe the differences seen in the boxplots.

Explanation of Solution

It is given in the question that the researchers want to know that can measurements of the petal length of flowers be of value when you need to determine the species of a certain flower.In the above graph, the box plot on the left box plot is for the species Versicolor and right box plot is for the species Virginica. We can say that depending on the plot, the petal of Versicolor is larger than Virginica. And the box plot of the Virginica seems to be more normally distributed than the box plot of the Vericolor.

(c)

To determine

To write a $95\%$ confidence interval for the difference in petal length.

Answer to Problem 28RE

The interval is $(10.167,14.433)$ .

Explanation of Solution

It is given in the question that the researchers want to know that can measurements of the petal length of flowers be of value when you need to determine the species of a certain flower.Thus, to find the confidence interval for mean we will use the calculator $\text{TI}-89$ . In the STAT Intsmenu, choose $4:2-$ SampTInt. You must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify the desired level of confidence.Thus, from the list given and by using the calculator $\text{TI}-89$ , the confidence interval will be as:

  $(10.167,14.433)$ .

(d)

To determine

To explain what your interval means.

Explanation of Solution

It is given in the question that the researchers want to know that can measurements of the petal length of flowers be of value when you need to determine the species of a certain flower. Thus, from the list given and by using the calculator $\text{TI}-89$ , the confidence interval will be as:

  $(10.167,14.433)$ .

So, we are $95\%$ confident that the difference of petal length of the species will be between $10.167\text{ and }14.433$ .

(e)

To determine

To explain is there evidence of a difference in petal length based on your interval.

Answer to Problem 28RE

Yes, there is evidence of a difference in petal length based on your interval.

Explanation of Solution

It is given in the question that the researchers want to know that can measurements of the petal length of flowers be of value when you need to determine the species of a certain flower. Thus, from the list given and by using the calculator $\text{TI}-89$ , the confidence interval will be as:

  $(10.167,14.433)$ .

So, we are $95\%$ confident that the difference of petal length of the species will be between $10.167\text{ and }14.433$ .As the lower limit of confidence interval is above zero, that is, it does not contain zero in the interval. Hence, we can that we are $95\%$ sure that the difference will not be zero. Yes, there is evidence of a difference in petal length based on your interval.