Chapter PVII, Problem 20RE

(a)

To determine

To make an appropriate display of these data.

Explanation of Solution

It is given in the question that Roper Reports asked the question from different age groups teens and record their responses. The table is as follows:

	Agree Completely	Agree somewhat	Neither disagree nor agree	Disagree somewhat	Disagree completely	Total
Teen	369	540	299	175	106	1489
30's	272	522	325	229	170	1518
60+	93	207	153	154	178	785
Total	734	1269	777	558	454	3792

Thus, the appropriate display of the data will be as:

  

Thus, by looking at the graph we can say that the teens and the other age groups have higher responses for agree somewhat option. The skewed of the bars are right skewed as the bars are smaller on the right.

(b)

To determine

To explain does a person’s age seem to affect their response to the question about nibbling.

Answer to Problem 20RE

There is insufficient evidence that a person’s age seem to affect their response to the question about nibbling.

Explanation of Solution

It is given in the question that Roper Reports asked the question from different age groups teens and record their responses. The table is as follows:

	Agree Completely	Agree somewhat	Neither disagree nor agree	Disagree somewhat	Disagree completely	Total
Teen	369	540	299	175	106	1489
30's	272	522	325	229	170	1518
60+	93	207	153	154	178	785
Total	734	1269	777	558	454	3792

Thus, to test a hypothesis of homogeneity or independence, we will use the calculator $\text{TI}-89$ so, we need to enter the data as a matrix. From the home screen, press APPS and select $6:$ Data/Matrix Editor, then select $3:$ New. Specify type as Matrix and name the matrix in the Variable box. Specify the number of rows and columns. Type the entries, pressing ENTER after each. Press $2\text{nd ESC}$ to leave the editor. To do the test, choose $\text{8:Chi2 2-way}$ from the STAT Tests menu. The hypothesis is defined as:

Null hypothesis: A person’s age do not affect their response to the question about nibbling.

Alternative hypothesis: A person’s age seem to affect their response to the question about nibbling.

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

  $\begin{array}{l}df=8\\ {\chi }^2=190.96\\ P>0.10\end{array}$

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,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude that there is insufficient evidence that a person’s age seem to affect their response to the question about nibbling.