1. A study is conducted to assess the relationship between cholesterol levels an

Question

1. A study is conducted to assess the relationship between cholesterol levels and coronary heart disease. 1329 adult aged subject's hospital records are randomly sampled. The cholesterol levels and chronic heart disease status of each subject is used. Cholesterol levels are classified into the ranges (0-199, (199-219], (220-259], and (260,300] mg/100cc, which correspond to levels Norma Above Normal, High, and Very High respectively. The 4x2 table of the 1329 observations is below: Cholestero CHD no CHD yes 307 12 31 Very High 24541 Normal Above Normal 246 439 High

Explanation / Answer

(e) null hypothesis H0: there is no association between cholesterol level and chd statu

alternate hypothesis H1: there is association between cholesterol level and chd status

(f) here we use chi-square test and chi-square=sum((O-E)2/E)=35.03 with (r-1)(c-1)=(4-2)*(2-1)=3df

is more than critical chi-square=7.81, (or p-value=0.000 less than 0.05 we reject null hypothess)

using ms-excel p-value=0.000 ( using ms-excel =CHIDIST(35.03,3) )

so we reject null hypothesis and conclude that there is association between cholesterol level and chd status

Observed(O) Expected (E) E (O-E) (O-E)2/E 307 1237*319/1329 296.9 10.08 0.34 246 1237*254/1329 236.4 9.58 0.39 439 1237*470/1329 437.5 1.54 0.01 245 1237*286/1329 266.2 -21.20 1.69 12 92*319/1329 22.1 -10.08 4.60 8 92*254/1329 17.6 -9.58 5.22 31 92*470/1329 32.5 -1.54 0.07 41 92*286/1329 19.8 21.20 22.70 sum= 1329 0 1329 0 35.03 critical chi-square= chi-square(0.05,3)= 7.81

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