Chapter PVII, Problem 26RE

To determine

To explain do these data indicate that continued treatment with infliximab is of value for Crohn’s disease patients who exhibit a positive initial response to the drug.

Answer to Problem 26RE

These data indicate that continued treatment with infliximab is of value for Crohn’s disease patients who exhibit a positive initial response to the drug.

Explanation of Solution

In the question, we have to test to find out that these data indicate that continued treatment with infliximab is of value for Crohn’s disease patients who exhibit a positive initial response to the drug. As in this data we are taking the sample from one only so it is the case of homogeneity. 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. So, the contingency table of the data given is as follows:

	Successes	Failure	Total
Group I	23	87	110
Group II	44	69	113
Group III	50	62	112
Total	117	218	335

And the hypothesis is defined as:

Null hypothesis: There is no difference in using infliximab on Crohn’s disease patients.

Alternative hypothesis: There is a difference in using infliximab on Crohn’s disease patients.

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

  $\begin{array}{l}{\chi }^2=14.96\\ df=2\\ P=0.0006\end{array}$

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 a difference in using infliximab on Crohn’s disease patients. So, these data indicate that continued treatment with infliximab is of value for Crohn’s disease patients who exhibit a positive initial response to the drug.