Chapter PVII, Problem 22RE

(a)

To determine

To explain is there evidence of an association and test an appropriate hypothesis and state your conclusion.

Answer to Problem 22RE

There is association between good grades in high school and family togetherness.

Explanation of Solution

It is given in the question that researcher wants to study that are good grades in high school associated with family togetherness. Thus, it is given in the regression analysis that,

  $\begin{array}{l}{R}^2=11\%\\ s=0.6682\\ df=140\end{array}$

Variable	Coefficient	SE(Coeff)
Intercept	2.7288	0.1148
Meals	0.1093	0.0263

  $\begin{array}{l}\overline{x}=3.78\\ S.D.=2.2\\ n=142\end{array}$

Thus, to test the hypothesis for mean we will use the calculator $\text{TI}-89$ . In the STAT Tests menu, choose $2:$

T -Test. You must specify whether you are using data stored in a list or whether you will enter the mean, standard deviation, and size of your sample. You must also specify the hypothesized model mean and whether the test is to be two-tail, lower-tail, or upper-tail. Select whether the test is to be simply computed or whether to display the distribution curve and highlight the area corresponding to the P-value of the test. The hypothesis is defined as:

Null hypothesis: There is no association.

Alternative hypothesis: There is association.

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

  $P\le 0.001$

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 association between good grades in high school and family togetherness.

(b)

To determine

To explain do you think this association would be useful in predicting a student’s grade point average.

Answer to Problem 22RE

This association would be useful in predicting a student’s grade point average.

Explanation of Solution

It is given in the question that researcher wants to study that are good grades in high school associated with family togetherness. Thus, it is given in the regression analysis that,

  $\begin{array}{l}{R}^2=11\%\\ s=0.6682\\ df=140\end{array}$

Variable	Coefficient	SE(Coeff)	t-ratio
Intercept	2.7288	0.1148	23.7700
Meals	0.1093	0.0263	4.1559

  $\begin{array}{l}\overline{x}=3.78\\ S.D.=2.2\\ n=142\end{array}$

The hypothesis is defined as:

Null hypothesis: This association would not be useful in predicting a student’s grade point average.

Alternative hypothesis: This association would be useful in predicting a student’s grade point average.

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

  $P\le 0.001$

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 thatthis association would be useful in predicting a student’s grade point average.

(c)

To determine

To explain are your answers to part (a) and (b) contradictory.

Answer to Problem 22RE

No, they are not.

Explanation of Solution

It is given in the question that researcher wants to study that are good grades in high school associated with family togetherness. Thus, it is given in the regression analysis that,

  $\begin{array}{l}{R}^2=11\%\\ s=0.6682\\ df=140\end{array}$

From part (a) and (b), we have the conclusion that there is association between good grades in high school and family togetherness and this association would be useful in predicting a student’s grade point average. So, the conclusions are not contradictory.