Chapter PVII, Problem 18RE

(a)

To determine

To explain do these data indicate that there is association between internet use and depression and test an appropriate hypothesis.

Answer to Problem 18RE

There is an association between internet use and depression.

Explanation of Solution

It is given in the question the researchers want to find out that is there any association between internet use and depression. Let us assume all the conditions and assumptions for the test are met. Thus, it is given that,

  $\begin{array}{l}{R}^2=4.6\%\\ s=0.4563\\ df=160\end{array}$

Variable	Coefficient	SE(coeff)	t-ratio	Prob
Constant	0.565485	0.0399	14.2	<0.0001
Intr_use	0.019948	0.0072	2.76	0.0064

The hypothesis is defined as:

Null hypothesis: There is no association between internet use and depression.

Alternative hypothesis: There is an association between internet use and depression.

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}P<0.0001\\ t=2.76\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P<0.05\Rightarrow \text{Reject }{H}_0$

Thus, we conclude that there is an association between internet use and depression.

(b)

To determine

To explain does this study support this conclusion.

Answer to Problem 18RE

No, this study does not support this conclusion.

Explanation of Solution

It is given in the question the researchers want to find out that is there any association between internet use and depression. Let us assume all the conditions and assumptions for the test are met. Thus, it is given that,

  $\begin{array}{l}{R}^2=4.6\%\\ s=0.4563\\ df=160\end{array}$

Variable	Coefficient	SE(coeff)	t-ratio	Prob
Constant	0.565485	0.0399	14.2	<0.0001
Intr_use	0.019948	0.0072	2.76	0.0064

One conclusion of the study was that those who spent more time online tended to be more depressed at the end of the experiment. News headlines said that too much time on the internet can lead to depression. The study does not support the conclusion because the study said that those who spent more time online tended to be depressed this does not said that spending time online leads to depression.

(c)

To determine

To explain is there evidence that the depression level of the subjects changed during this study.

Answer to Problem 18RE

The depression level of the subjects changed during this study.

Explanation of Solution

It is given in the question the researchers want to find out that is there any association between internet use and depression. Let us assume all the conditions and assumptions for the test are met. Thus, it is given that,

  $\begin{array}{l}{R}^2=4.6\%\\ s=0.4563\\ df=160\end{array}$

Variable	Coefficient	SE(coeff)	t-ratio	Prob
Constant	0.565485	0.0399	14.2	<0.0001
Intr_use	0.019948	0.0072	2.76	0.0064

The hypothesis is defined as:

Null hypothesis: The depression level of the subjects does not change.

Alternative hypothesis: The depression level of the subjects change.

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}P<0.0001\\ t=2.76\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P<0.05\Rightarrow \text{Reject }{H}_0$

Thus, we conclude that the depression level of the subjects changed during this study.