Chapter 4.2, Problem 76E

(a)

To determine

To construct a comparative dot plot of the data and describe what you see.

Explanation of Solution

A comparative dot plot of the data given in the question is as follows:

For the Active data:

  

And for the Inactive data set:

  

Thus, by looking at the dot plots, we can say that the Active dot plot contains gaps, while the Inactive dot plot does not. The spread is larger for the Active data. The center is higher for the Active data, because the Active data take on higher values in general. The Active data seem to be symmetrically distributed, while the Inactive data are right-skewed.

(b)

To determine

To calculate the mean change in pain rating for each group and find the difference in the average changes for the two groups (Active minus Inactive).

Answer to Problem 76E

  ${\overline{x}}_d=4.1462$ .

Explanation of Solution

In the question the active and the inactive data sets are given for the pain reliefs of the patients. Thus, the mean of the Active data set is calculated as:

  $\begin{array}{l}{\overline{x}}_A=\frac{\begin{array}{l}10+6+1+10+6+8+5+5+6+8+7+8+7+6+4+4+7+10+6+10+6+5+5+1\\ +0+0+0+0+1\end{array}}{29}\\ =5.2414\end{array}$

And the mean of the Inactive data can be calculated as:

  $\begin{array}{l}{\overline{x}}_B=\frac{4+3+5+2+1+4+1+0+0+1+0+0+0+0+0+0+0+1+0+0+1}{21}\\ =1.0952\end{array}$

Thus, the difference between the means of the Active and the Inactive data is as:

  $\begin{array}{l}{\overline{x}}_d={\overline{x}}_A-{\overline{x}}_B\\ =5.2414-1.0952\\ =4.1462\end{array}$

(c)

To determine

To describe how you could use index cards to randomly assign the subjects to the treatment groups.

Explanation of Solution

In the question the active and the inactive data sets are given for the pain reliefs of the patients. Thus, we can use index cards to randomly assign the subjects to the treatment groups as:

First, write the numbers $\text{1 and 2}$ each on a different slip of paper. Then, lie the papers on a table with the numbers facing down. And then, mix the papers until you no longer know which number is where on the table. Now, pick one of the slips of paper, the treatment corresponding to the number will then be used for the subject. And repeat till all subjects have received a treatment.

(d)

To determine

To explain what conclusion would you draw about the effect of magnets on pain relief.

Explanation of Solution

In the question the active and the inactive data sets are given for the pain reliefs of the patients. Thus, the conclusion we can draw about the effect of magnets on pain relief is that in the dot plot, we note that the difference for the average change in pain rating can be both positive and negative and thus there is no statistically significant effect of magnets on pain relief.