Chapter 11.6, Problem 2E

To determine

To find: the question which is different

Answer to Problem 2E

The different question is

“What is the square root of the average of the squared differences from $-2.85$ ”

Explanation of Solution

Given:

Weight of tumor (grams)
Control group	3.3	3.2	3.7	3.5	3.3	3.4
Treatment group	0.4	0.6	0.5	0.6	0.7	0.5

Calculation:

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

Thus, 1st 2nd and 4th questions are actually same.

Thus, $\text{Experimental mean }={\overline{x}}_{treatment}-{\overline{x}}_{control}$

Now,

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

So,

  $\begin{array}{l}{\overline{x}}_{control}=\frac{3.3+3.2+3.7+3.5+3.3+3.4}{6}\\ =3.4\\ {\overline{x}}_{treatment}=\frac{0.4+0.6+0.5+0.6+0.7+0.5}{6}\\ =0.55\end{array}$

Thus,

  $\begin{array}{l}\text{Experimental mean }={\overline{x}}_{treatment}-{\overline{x}}_{control}\\ =0.55-3.4\\ =-2.85\end{array}$

The 3rd question is a different question.

The average of the squared differences from the mean that is -2.85 is called the variance.

And the square root of the variance is the standard deviation.

The square root of the average of the squared differences from -2.85 is about 5.03.

Conclusion:

Therefore,the 3rd question is a different question.