Q. 26 - The Practice of Statistics for AP

Question

Angry people and heart disease People who get angry easily tend to have more heart disease. That’s the conclusion of a study that followed a random sample of $12,986$ people from three locations for about four years. All subjects were free of heart disease at the beginning of the study. The subjects took the Spiel burger Trait Anger Scale test, which measures how prone a person is to sudden anger. Here are data for the $8474$ people in the sample who had normal blood pressure. CHD stands for “coronary heart disease. ”This includes people who had heart attacks and those who needed medical treatment for heart disease.

Do these data support the study’s conclusion about the relationship between anger and heart disease? Follow the four-step process.

Step-by-Step Solution

Answer

Yes, the data support the conclusion of anger and heart disease.

Step 1: Given information

The provided information 

	Low anger	Moderate anger	High anger	Total
CHD No CHD	53 3057	110 4621	27 606	190 8284
Total	3110	4731	633	8474

The table is provided to determine if there is an association between anger and heart, disease. The process will determine the conditional distribution of heart disease among the different categories of anger.

Step 2: Concept

There is a real-world scenario for a statistical problem. The four processes of state, plan, do, and conclusions can be used to organize a variety of situations.

Step 3: Explanation

The rage intensity conditional distribution of people without CHD is shown below. 

The conditional distribution of people with No CHD ad anger intensity
Anger intensity	No CHD	Percentage
Low anger	3057	$\frac{3057}{8284}\times 100$	36.90
Moderate anger	4621	$\frac{4621}{8284}\times 100$	55.78
High anger	606	$\frac{606}{8284}\times 100$	7.31
Total	8284	$\frac{8284}{8284}\times 100$	100

The following is a conditional distribution comparison table: 

The conditional distribution of people with CHD or No CHD ad anger intensity
Anger intensity	CHD	No CHD	Percentage
Low anger	$\frac{53}{190}\times 100$	27.89	$\frac{3057}{8284}\times 100$	36.90
Moderate anger	$\frac{110}{190}\times 100$	57.89	$\frac{4621}{8284}\times 100$	55.78
High anger	$\frac{27}{190}\times 100$	14.21	$\frac{606}{8284}\times 100$	7.31
Total	$\frac{190}{190}\times 100$	100	$\frac{8284}{8284}\times 100$	100

 We'll build a side-by-side bar graph comparing the anger level of those with and without CHD. 

Around $37\%$ of persons with low anger do not have CHD, which is higher than the $37\%$ of people with CHD ($27.89$ percent vs $36.90$ percent ). The percentage of those with moderate anger does not differ ($57.89$ percent vs $55.78$ percent ). However, approximately $14\%$ of persons with high anger have CHD, which is nearly double the number of people without CHD ($14.21$ percent vs $7.32$ percent ).

As a result, the statistics back up the study's findings of the link between rage and heart disease.