Q. 41 - The Practice of Statistics for AP

Question

Perform a follow-up analysis of the test in Exercise 39 by finding the individual components of the chi-square statistic. Which cell(s) contributed most to the final result? 

Step-by-Step Solution

Answer

It is noted that the highest chi-square totals are for the Patch plus drug. This means that the treatment Patch plus drug gives the best results and thus this treatment should be used (if the side effects are not too bad).

Step 1: Given information

The given data is 

Step 2: Explanation

Observed counts

Expected count 

The chi-square statistic is the sum of squared deviations (between observed and expected counts) divided by the expected count:

$$\begin{gathered} {\chi }^2=\frac{(40-61.7514{)}^2}{61.7514}+\frac{(74-61.7514{)}^2}{61.7514}+\frac{(87-62.0045{)}^2}{62.0045}+\frac{(25-40.4927{)}^2}{40.4927} \\ +\frac{(204-182.2486{)}^2}{182.2486}+\frac{(170-182.2486{)}^2}{182.2486}+\frac{(158-182.9955{)}^2}{182.9955}+\frac{(135-119.5073{)}^2}{119.5073} \\ =7.662+2.430+10.076+5.928+2.596+0.823+3.414+2.008 \\ =34.937 \end{gathered}$$

We note that the highest chi-square totals are for the Patch plus drug. This means that the treatment Patch plus drug gives the best results and thus this treatment should be used (if the side effects are not too bad).