Question

Friedman and Rosenman have suggested that personality type isrelated to heart disease. specifically, type A people, who arecompetitive, driven, pressured and impatient are more prone toheart disease. on the other hand, type B people, who are lesscompetitive and more relaxed are less likely to have heart disease.suppose that an investigator would like to examine the relationshipbetween personality type and disease. for a random sample ofindividuals, personality type is assessed witha standardizedtest. these people are then examined and categorized as to whetherthey have a heart disorder. the observed frequencies are asfollows: noheart disease heartdiseaseTypeA 32 18 50TypeB 128 22 150 160 40is there any relationship between personality and disorder? testat the .05 level of significance.

Answer 1

since p value(0.001091 ) is less than less than alpha(0.05)

null hypothesis H₀ is rejected.

Hence, we conclude that there is a relationship between personality and disorder.

Explanation:

Given the data in the question;

non-heart disease heart disease total

TypeA 32 18 50

TypeB 128 22 150

total 160 40

level of significance ∝ = 0.05

H₀ : There is no relationship between personality and disorder

H₁ : There is a relationship between personality and disorder

so

the computational table for x²

E₁ = 50×160 / 200 = 40

O E O-E (O-E)² (O-E)² /E

32 40 -8 64 1.6

18 10 8 64 6.4

128 120 8 64 0.5333

22 30 -8 64 2.133

∑ 10.667

so

X² = ∑( (O-E)² /E ) = 10.667

The contingency table is 2×2, since there are 2 rows and 2 columns

df = (2-1)(2-1) = 1

P Value from Chi-Square Calculator

Chi-square score: 10.667

DF : 1

p-value = 0.001091

since p value(0.001091 ) is less than less than alpha(0.05)

null hypothesis H₀ is rejected.

Hence, we conclude that there is a relationship between personality and disorder.