Question

How to quit smoking Refer to Exercise $37$. Which treatment seems to be most effective? Least effective? Justify your choices.

Short answer

The most effective treatment is a patch plus drug and the least effective is a Nicotine patch.

Step-by-step solution

Given information

We need to find the most effective and least effective treatment to quit smoking.

Explanation

We know that

Expected frequencies are a product of row and column total divided by table total. So,

ROW AND COLUMN NUMBER	EXPECTED FREQUENCY
$E_{11}$	$61.75$
$E_{12}$	$182.25$
$E_{21}$	$61.75$
$E_{22}$	$182.25$
$E_{31}$	$62.00$
$E_{32}$	$183.00$
$E_{41}$	$40.49$

$E_{42}$

$119.51$

For the treatment Nicotine patch, the predicted frequency of the number of successes deviates the greatest from the observed frequency, despite the fact that the expected frequency is higher than the observed frequency (expected $61.75$and observed $40$). As a result, the Nicotine Patch is the least effective treatment option.

We note that for the therapy Patch plus medicine, the predicted frequency of the number of successes deviates the most from the observed frequency, while the expected frequency is lower than the observed frequency (expected $62.00$and observed $87$). As a result, the most successful treatment is the Patch with medication.