Chapter 11.6, Problem 8E

To determine

To find: the difference of the forms.

Answer to Problem 8E

The Experimental difference is -0.1.

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:

In this question you have to resample the data given in question4. 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.

Treatment group	34.6	35.4	33	34.6	35.2	35.2	36.2	35
Assigned number	1	2	3	4	5	6	7	8

Treatment group	31.4	33	32.4	32.6	33.4	33.4	34.8	33
Assigned number	9	10	11	12	13	14	15	16

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.

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

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	33	35.8	32.6	34.6	34.8	36.2	32.4	33
New treatment group	34.6	31.4	35.2	33.4	35.4	33	35.2	33.4

The mean score of the new control group is given by

  $\begin{array}{l}{\overline{x}}_{control}=\frac{33+35.8+32.6+34.6+34.8+36.2+32.4+33}{8}\\ =\frac{272.4}{8}\\ =34.05\end{array}$

The mean score of the new treatment group is given by

  $\begin{array}{l}{\overline{x}}_{treatment}=\frac{34.6+31.4+35.2+33.4+35.4+33+35.2+33.4}{8}\\ =\frac{271.6}{8}\\ =33.95\end{array}$

New Experimental difference

  $\begin{array}{l}{\overline{x}}_{treatment}-{\overline{x}}_{control}=33.95-34.05\\ =-0.1\end{array}$

Conclusion:

Therefore,the Experimental difference is -0.1.