Chapter 2, Problem 170E

(a)

Section 1:

To determine

To find: The two-way table for the data set.

Answer to Problem 170E

Solution: The table that represents the dead and alive smokers and dead and alive nonsmokers is provided below:

Category	Dead	Alive
Smoker	139	443
Non-smoker	230	502

Explanation of Solution

Calculation: To obtain the two-way table, the dead and alive persons of each group are clustered according to the smoker and nonsmoker group.

There are 19 dead smokers in age group 18 to 44, 78 dead smokers in the age group 45 to 65, and 42 dead smokers in age group 65 and more. So, there are $19+78+42=139$ dead smokers.

Similarly, there are 13 dead nonsmokers in the age group 18 to 44, 52 dead nonsmokers in the age group 45 to 65, and 165 dead nonsmokers in the age group 65 and more. So, there are $13+52+165=230$ dead nonsmokers.

There are 269 alive smokers in age group 18 to 44, 167 alive smokers in the age group 45 to 65, and 7 alive smokers in age group 65 and more. So, there are $269+167+7=443$ smokers who were alive.

Similarly, there are 327 alive nonsmokers in the age group 18 to 44, 147 alive nonsmokers in the age group 45 to 65, and 28 alive nonsmokers in the age group 65 and more. Hence, there are $327+147+28=502$ dead nonsmokers.

The data can be represented in the form of two-way table as provided below:

Category	Dead	Alive
Smoker	139	443
Non-smoker	230	502

Section 2:

To determine

To find: The percent of smokers stayed alive after 20 years.

Answer to Problem 170E

Solution: The percent of smokers who are alive after age of 20 years is 76.11%.

Explanation of Solution

Calculation: There are total 1314 number of women participated in the survey. And the percent of smokers who were alive after age of 20 years are obtained as a ratio of the number of alive women who smokes and total participated women.

Therefore, the required percentage is calculated as:

$\begin{array}{c}\text{Percentage}=\frac{\text{Number of smokers alive}}{\text{Total number of smokers}}\\ =\frac{443}{443+139}\times 100\\ =\frac{443}{582}\times 100\\ =76.11\%\end{array}$

Section 3:

To determine

To find: The percent of nonsmokers stayed alive after the age of 20 years.

Answer to Problem 170E

Solution: The percent of nonsmokers who alive after the age of 20 years is 68.58%.

Explanation of Solution

Calculation: There are total 1314 number of women participated in the survey. The percent of nonsmokers who are alive after the age of 20 years are obtained as a ratio of the number of alive women who are nonsmokes and total participated women.

Therefore, the required percentage is calculated as:

$\begin{array}{c}\text{Percentage}=\frac{\text{Number of non-smokers alive}}{\text{Total number of non-smokers}}\\ =\frac{502}{230+502}\times 100\\ =\frac{502}{732}\times 100\\ =68.58\%\end{array}$

Section 4:

To determine

To explain: Whether it is astonishing that a greater percent of smokers remained alive.

Answer to Problem 170E

Solution: No, the obtained result is not astonishing.

Explanation of Solution

The lurking variables are often effect the result of the study if it is not controlled or taken into consideration. In the provided scenario, the age of the women can be considered as the lurking variable. But it is not considered when the percentage of women who alive after 20 years for the smokers and nonsmokers. So, the obtained result is not surprising.

(b)

To determine

To find: The higher percent of alive nonsmoker within each age group.

Answer to Problem 170E

Solution: There is higher percentage of the nonsmokers women who are alive 20 years later.

Explanation of Solution

Calculation: To show that within the particular age group a greater percent of nonsmokers stayed alive after 20 years, the percentage of alive women in each age group for both the cases of smoker and nonsmoker is calculated. To obtain the required percentage, below steps are followed in Minitab software.

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat > Tables > Descriptive Statistics.

Step 3: Select “Smoker” in “For rows” and select “Age” in “For columns”. Select “Outcome” in “For the layers”. And select “Count” in “Frequencies are in”.

Step 4: Select the option “Column percent” and under the “Categorical Variables”.

Step 5: Click OK twice.

The obtained percentage are shown in the below table.

	18 years to 44 years		45 years to 64 years		More than 65 years
	Smoker	Nonsmoker	Smoker	Nonsmoker	Smoker	Nonsmoker
Dead	59.38	40.63	60.00	40.00	20.29	79.71
Alive	45.13	54.87	53.18	46.82	20.00	80.00

From the above obtained result, it can be concluded that there is more percentage of women who are alive 20 years later within each age group.

(c)

To determine

To test: The explanation provided by the author of the study.

Answer to Problem 170E

Solution: From the obtained percentage it can be said that the older women who were smokers died due to the age and it verifies the explanation provided by the author of the study.

Explanation of Solution

Calculation: To show that the lower percentage of the smoker’s women stayed alive after 20 years, the percentage alive and dead smokers in each age group for both the cases of smoker and nonsmoker is calculated. To obtain the required percentage, below steps are followed in Minitab software.

Step 1: Enter the data in Minitab worksheet.

Step 2: Go to Stat > Tables > Descriptive Statistics.

Step 3: Select “Smoker” in “For rows” and select “Count” in “For columns”. Select “Age” in “For the layers”. And select “Count” in “Frequencies are in”.

Step 4: Select the option “Total percents” and under the “Categorical Variables”.

Step 5: Click OK twice.

The obtained percentage are shown in the below table.

	18 years to 44 years	45 years to 64 years	More than 65 years
Dead	3.03	17.57	17.36
Alive	42.83	37.61	2.89

There are 17.36% women who died at the time of follow-up but the percentage of the women alive is 2.89. The death is more common for the elderly women and the effect of smoking is less on the women whose age is more than 65 years. So, it can be said that the percentage of death is more for the women of 65+ due to the age.

Interpretation: The higher percentage of smoker women died at the time of follow up due to the effect of age.