Chapter 11.6, Problem 4E

(a)

To determine

To find: themean circumference of the control group.

Answer to Problem 4E

The mean circumference of the control group is 34.9.

Explanation of Solution

Given:

Circumference (inches)
Control group	34.6	35.4	33	34.6
Treatment group	31.4	33	32.4	32.6

Circumference (inches)
Control group	35.2	35.2	36.2	35
Treatment group	33.4	33.4	34.8	33

Calculation:

The mean $\overline{x}$ is found using the formula

  $\overline{x}=\frac{{\displaystyle \sum x}}{n}$

Here,

  ${\displaystyle \sum x}$ represents, sum of all the given number.

And n represents, how many numbers are there in the sample.

The mean circumference of the control group is given by

  $\begin{array}{l}{\overline{x}}_{control}=\frac{34.6+35.4+33+34.6+35.2+35.2+36.2+35}{8}\\ =\frac{279.2}{8}\\ =34.9\end{array}$

Conclusion:

Therefore, the mean circumference of the control group is 34.9.

(b)

To determine

To find: the mean circumferenceof the treatment group.

Answer to Problem 4E

The mean circumference of the treatment group is 33.

Explanation of Solution

Calculation:

The mean circumference of the treatment group is given by

  $\begin{array}{l}{\overline{x}}_{treatment}=\frac{31.4+33+32.4+32.6+33.4+33.4+34.8+33}{8}\\ =\frac{264}{8}\\ =33\end{array}$

Conclusion:

Therefore, the mean circumference of the treatment group is 33.

(c)

To determine

To find: the experimental difference of the means.

Answer to Problem 4E

The experimental difference of the mean is -1.9.

Explanation of Solution

Calculation:

Experimental difference of the mean is the difference of the mean of treatment group and the mean of the control group.

Thus,

  $\begin{array}{l}\text{Experimental mean }={\overline{x}}_{treatment}-{\overline{x}}_{control}\\ =33-34.9\\ =-1.9\end{array}$

Conclusion:

Therefore, the experimental difference of the mean is -1.9.

(d)

To determine

To display: the data in a double dot plot.

Answer to Problem 4E

  

Explanation of Solution

Calculation:

Double dot plot for the given data is

  

Conclusion:

Therefore, the Double dot plot is displayed.

(e)

To determine

To explain: the conclusion.

Answer to Problem 4E

It is concluded that the low-level laser therapy may be slightly effective in reducing the waist circumference of adults.

Explanation of Solution

Calculation:

The plot of the data shows that the two data sets tend to be fairly symmetric and have outliers.

Thus, It is concludedthat the low-level laser therapy may be slightly effective in reducing the waist circumference of adults.

Conclusion:

Therefore, It is concludedthat the low-level laser therapy may be slightly effective in reducing the waist circumference of adults.