Chapter 11.6, Problem 7E

To determine

To calculate: the difference of the forms.

Answer to Problem 7E

The Experimental difference is -2.375.

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:

In this question you have to resample the data given in question 3. And calculate new mean.

To resample the data, the first step is to combine the measurements from both groups and assign a number to each value. Let the numbers 1 through 8 represent the data in the original control group, and let the numbers 9 through 16 represent the data in the original treatment group, as shown.

Given:

Control group	49	45	43	46	45	46	47	46
Assigned number	1	2	3	4	5	6	7	8	8

Control group	39	40	39	37	41	40	42	43
Assigned number	9	10	11	12	13	14	15	16	8

Now, use a random number generator. Randomly generate 16 numbers from 1 through 16 without repeating a number.

(For this, you can use the TI-84 Plus calculator.

Press

Pressthree times to reach the PRB menu.

Select 8: randIntNoRep(

Press

Press

)

The table shows the results.

13	5	3	4	6	15	7	16
11	10	2	12	14	8	9	1

Use the first 8 numbers to make the new control group, and the next 8 to make the new treatment group. The results are shown in the table below.

New control group	41	46	43	47	45	42	47	43
New treatment group	39	40	45	37	40	46	39	49

The mean score of the new control group is given by

  $\begin{array}{l}{\overline{x}}_{control}=\frac{41+46+43+47+45+42+47+43}{8}\\ =\frac{354}{8}\\ =44.25\end{array}$

The mean score of the new treatment group is given by

  $\begin{array}{l}{\overline{x}}_{treatment}=\frac{39+40+45+37+40+46+39+49}{8}\\ =\frac{335}{8}\\ =41.875\end{array}$

New Experimental difference

  $\begin{array}{l}{\overline{x}}_{treatment}-{\overline{x}}_{control}=41.875-44.25\\ =-2.375\end{array}$

Conclusion:

Therefore,the Experimental difference is -2.375.