Question

12.1. People who get angry easily rend to have more heart disease. That's the conclusion of a study followed by a random sample of 12,986 people from three locations for about four years All the subjects were free of heart disease at the beginning of the study. The subjects took the Spielberger 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 CHD No CHD Low Anger 53 3057 Moderate Anger High Anger 110 4621 27 606 Do these data support the study's conclusion about the relationship between anger and heart disease?

Answer 1

The null and alternative hypothesis is

H0: There is no relationship between anger and heart disease.

H1: Ther is a relationship between anger and heart disease.

Level of significance = 0.05

Test statistic is

$\chi ^{2}=\sum \frac{(O-E)^{2}}{E}$

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

O	E	(O-E)	(O-E)^2	(O-E)^2/E
53	69.73094	-16.7309	279.9244	4.01435
110	106.0762	3.923767	15.39595	0.14514
27	14.19283	12.80717	164.0237	11.55681
3057	3040.269	16.73094	279.9244	0.092072
4621	4624.924	-3.92377	15.39595	0.003329
606	618.8072	-12.8072	164.0237	0.265064
			Total	16.08

$\chi ^{2}=\sum \frac{(O-E)^{2}}{E} =16.08$

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (3 - 1) = 1 * 2 = 2

Critical value = 5.991

( From chi-square table)

Test statistic > critical value we reject null hypothesis.

Conclusion:

There is a relationship between anger and heart disease.