Chapter 11.6, Problem 3E

(a)

To determine

To find: themean score of the control group.

Answer to Problem 3E

The mean score of the control group is 46.

Explanation of Solution

Given:

Depression score
Control group	49	45	43	47
Treatment group	39	40	39	37

Depression score
Control group	46	45	47	46
Treatment group	41	40	42	43

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 score of the control group is given by

  $\begin{array}{l}{\overline{x}}_{control}=\frac{49+45+43+47+46+45+47+46}{8}\\ =\frac{368}{8}\\ =46\end{array}$

Conclusion:

Therefore, the mean score of the control group is 46.

(b)

To determine

To find: the mean scoreof the treatment group.

Answer to Problem 3E

The mean score of the treatment group is 35.125.

Explanation of Solution

Calculation:

The mean score of the treatment group is given by

  $\begin{array}{l}{\overline{x}}_{treatment}=\frac{39+40+39+37+41+40+42+43}{8}\\ =\frac{281}{8}\\ =35.125\end{array}$

Conclusion:

Therefore, the mean score of the treatment group is 35.125.

(c)

To determine

To find: the experimental difference of the means.

Answer to Problem 3E

The experimental difference of the mean is -10.875.

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,

  $\begin{array}{l}\text{Experimental mean }={\overline{x}}_{treatment}-{\overline{x}}_{control}\\ =35.125-46\\ =-10.875\end{array}$

Conclusion:

Therefore, the experimental difference of the mean is -10.875.

(d)

To determine

To display: the data in a double dot plot.

Answer to Problem 3E

  

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 3E

It is concluded that the music therapy may be effective in reducing depression scores of college students.

Explanation of Solution

Calculation:

The plot of the data shows that the two data sets tend to be fairly symmetric and have no extreme values (outliers). So, the mean is a suitable measure of center.

Thus, It is concludedthat the music therapy may be effective in reducing depression scores of college students.

Conclusion:

Therefore, It is concludedthat the music therapy may be effective in reducing depression scores of college students.