Chapter PVII, Problem 29RE

To determine

To explain what would you recommend to them about the prospects for marketing their new cracker.

Answer to Problem 29RE

The prospects for marketing are not good.

Explanation of Solution

In the question, the contingency table for the cracker and bloat is given and we have to test whether we will recommend the prospects for marketing their new cracker. Let us define the hypothesis as:

Null hypothesis: There is no association between cracker type and bloating.

Alternative hypothesis: There is an association between cracker type and bloating.

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 contingency table is given in the question.

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

  $\begin{array}{l}{\chi }^2=8.23\\ df=3\\ P=0.0414\end{array}$

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 cracker type and bloating. Since there is association between them then prospects for marketing are not good.