Question

It’s hard for smokers to quit. Perhaps prescribing a drug to fight

depression will work as well as the usual nicotine patch. Perhaps combining the patch and

the drug will work better than either treatment alone. Here are data from a randomized,

double-blind trial that compared four treatments.

A “success” means that the subject did not smoke for a year following the start of the study.

a. Summarize these data in a two-way table.

b. Do the data provide convincing evidence of a difference in the effectiveness of the four

treatments at the$\alpha =0.05$significance level?

Short answer

(a) To construct the two-way table, let the treatments be given in the rows and let the successes/failures be given in the columns.

(b)We dismiss invalid and conclude there's adequate prove that the victory rate depends on treatment type. I.e., there's distinction within the adequacy of four treatments.

Step-by-step solution

Part (a) Step 1: Given informantion

We have been given the data of smokers and which of them quit.

Part(a) Step 2: Explanation

To construct the two-way table, let the treatments be given in the rows and let the successes/failures be given in the columns.

We then already know the number of successes for each treatment and the row totals (which are the number of subjects). The number of failures is then the row total decreased by the number of successes. The column totals is the sum of all counts in the column.

	Nicotine	Drug	Nicotine+Drug	Placebo
Success	$43$	$81$	$93$	$33$	$250$
Failure	$205$	$167$	$137$	$137$	$666$
	$248$	$248$	$170$	$170$	$916$

Part(b) Step 1: Given information

We have been given the data of smokers and which of them quit.

Part(b) Step 2: Explanation

$$\begin{gathered} {\chi }^2={\sum }_i (o_i-e_i{)}^2/e_i=33.67 \\ (o_i:┤obsvd,e_i:expected) \\ p-value=P({\chi }_{"}tf-3{"}^2>33.67)=2.32*{10}^{(}-7)<<0.05 \end{gathered}$$

So we dismiss invalid and conclude there's adequate prove that the victory rate depends on treatment type. I.e., there's distinction within the adequacy of four treatments.