Chapter 11, Problem 8CT

(a)

To determine

To find: The mean yields of the control group and treatment group.

Answer to Problem 8CT

The mean yields of the control group and treatment group

  $\overline{x}control=1.025$

  $\overline{x}treatmentl=1.125$

Explanation of Solution

Given:

Bone density (g/cm²)

Control group	$0.9$	$1.2$	$1.0$	$0.8$	$1.3$	$1.1$	$0.9$	$1.0$
Treatment group	$1.2$	$1.0$	$0.9$	$1.3$	$1.2$	$0.9$	$1.3$	$1.2$

Calculation:

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

  $\overline{x}=\frac{\Sigma x}{n}$

Here $\Sigma x$ represents the sum of all given numbers.

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

The mean yield of the control group is given by

  $\begin{array}{l}\overline{x}control=\frac{0.9+1.2+1.0+0.8+1.3+1.1+0.9+1.0}{8}\\ =\frac{8.2}{8}\\ =1.025\end{array}$

The mean score of the treatment group is given by

  $\begin{array}{l}\overline{x}treatmentl=\frac{1.2+1.0+0.9+1.2+1.2+0.9+1.3+1.2}{8}\\ =\frac{9}{8}\\ =1.125\end{array}$

Conclusion:

Hence, the mean yields of the control group and treatment group are

  $\overline{x}control=1.025$ , $\overline{x}treatmentl=1.125$

(b)

To determine

To find: The experimental difference of the means.

Answer to Problem 8CT

The experimental difference of the means is $0.1$

Explanation of Solution

Given:

Bone density (g/cm²)

Control group	$0.9$	$1.2$	$1.0$	$0.8$	$1.3$	$1.1$	$0.9$	$1.0$
Treatment group	$1.2$	$1.0$	$0.9$	$1.3$	$1.2$	$0.9$	$1.3$	$1.2$

Calculation:

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

Thus,

  $\begin{array}{l}Experimentalmean=\overline{x}treatmentl-\overline{x}control\\ =1.125-1.025\\ =0.1\end{array}$

Conclusion:

Hence, the experimental difference of the means is $0.1$

(c)

To determine

To display: The data in double dot plot.

Answer to Problem 8CT

  

It is concluded that the vitamin supplement has no effect on bone density.

Explanation of Solution

Given:

Bone density (g/cm²)

Control group	$0.9$	$1.2$	$1.0$	$0.8$	$1.3$	$1.1$	$0.9$	$1.0$
Treatment group	$1.2$	$1.0$	$0.9$	$1.3$	$1.2$	$0.9$	$1.3$	$1.2$

Calculation:

Double dot plot for the given data is

  

From the above double dot plot you can conclude that the vitamin supplement has no effect on bone density.

Conclusion:

Hence, the double dot plot is displayed and concluded that the vitamin supplement has no effect on bone density.

(d)

To determine

To find: The conclusion about the hypothesis.

Answer to Problem 8CT

The hypothesis is probably true.

Explanation of Solution

Given:

Bone density (g/cm²)

Control group	$0.9$	$1.2$	$1.0$	$0.8$	$1.3$	$1.1$	$0.9$	$1.0$
Treatment group	$1.2$	$1.0$	$0.9$	$1.3$	$1.2$	$0.9$	$1.3$	$1.2$

Calculation:

The hypothesis is probably true.

The hypothesis assumes the difference of the mean is $0$ and the difference in part $(b)$ is less than $1$ standard deviation from the mean.

Conclusion:

Hence, The hypothesis is probably true and the difference of the mean is $0$ and the difference in part $(b)$ is less than $1$ standard deviation from the mean.