To determine whether baldness causes coronary heart disease (CHD) in men, a hypo
ID: 3309305 • Letter: T
Question
To determine whether baldness causes coronary heart disease (CHD) in men, a hypothetical cohort study was carried out. The epidemiologist in charge of the study recruited 10,000 bald men and 10,000 men with hair into the study and followed all of them for 10 years to determine whether they developed CHD. Results are shown below.
The relative risk of CHD associated with baldness = 4.0789.
Question: Does this result suggest that baldness may be a cause of CHD? Why or why not?
CHD Yes No Total Bald (exposed) 775 9,225 10,000 Hairy (non-exposed) 190 9,810 10,000 Total 965 19,035 20,000Explanation / Answer
No, this result suggest that baldness may be a cause of CHD, because baldness causes coronary heart disease (CHD) in men, a hypothetical cohort study was carried out.
Given table data is as below MATRIX col1 col2 TOTALS row 1 775 9225 10000 row 2 190 9810 10000 TOTALS 965 19035 N = 20000 ------------------------------------------------------------------calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N ------------------------------------------------------------------
expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 482.5 9517.5 row 2 482.5 9517.5 ------------------------------------------------------------------
calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 775 482.5 292.5 85556.25 177.319 9225 9517.5 -292.5 85556.25 8.989 190 482.5 -292.5 85556.25 177.319 9810 9517.5 292.5 85556.25 8.989 ^2 o = 372.616 ------------------------------------------------------------------
set up null vs alternative as
null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =3.841
since our test is right tailed,reject Ho when ^2 o > 3.841
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 372.616
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.841
we got | ^2| =372.616 & | ^2 | =3.841
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0
ANSWERS
---------------
null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
test statistic: 372.616
critical value: 3.841
p-value:0
decision: reject Ho
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