The Physicians\' Health Study randomly assigned 22,071 healthy male physicians a

Question

The Physicians' Health Study randomly assigned 22,071 healthy male physicians at least 40 years old to take either an aspirin every other day or a placebo pill every other day. Of the 11711 physicians who took aspirin regularly for 5 years, 10 had a fatal heart attack and 139 had a nonfatal heart attack. Of the 10360 who took the placebo, 27 suffered a fatal heart attack and 213 had a nonfatal heart attack. Please use 4 decimal places to answer the questions below.

(a) What is the proportion of physicians who suffered a fatal heart attack in the:

aspirin group?   
placebo group?  

(b) Calculate the relative risk of a fatal heart attack for physicians taking aspirin compared with those taking a placebo (do not use the rounded values from part (a) to do your calculations. Use the original proportions in your calculation. Remember, give your answer to 4 decimal places.).
  

(c) What is the proportion of physicians who suffered a nonfatal heart attack in the:

aspirin group?  
placebo group?

(d) Calculate the relative risk of a nonfatal heart attack, for physicians taking aspirin compared with those taking a placebo (do not use rounded values in your calculation and give your answer to 4 decimal places).

Explanation / Answer

a.
the proportion of physicians who suffered a fatal heart attack in the
aspirin group:
sample one, x1 =10, n1 =11711, p1= x1/n1=0.0009
placebo group:
sample two, x2 =27, n2 =10360, p2= x2/n2=0.0026

b.
the relative risk of a fatal heart attack for physicians taking aspirin compared with those taking a placebo

Given that,
sample one, x1 =10, n1 =11711, p1= x1/n1=0.0009
sample two, x2 =27, n2 =10360, p2= x2/n2=0.0026
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.001-0.0026)/sqrt((0.002*0.9983(1/11711+1/10360))
zo =-3.1757
| zo | =3.1757
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =3.176 & | z | =1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -3.1757 ) = 0.0015
hence value of p0.05 > 0.0015,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: -3.1757
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.0015
c.
the proportion of physicians who suffered a nonfatal heart attack in the
aspirin group :
sample one, x1 =139, n1 =11711, p1= x1/n1=0.0119
placebo group :
sample two, x2 =213, n2 =10360, p2= x2/n2=0.0206

d.
the relative risk of a nonfatal heart attack, for physicians taking aspirin compared with those taking a placebo

Given that,
sample one, x1 =139, n1 =11711, p1= x1/n1=0.0119
sample two, x2 =213, n2 =10360, p2= x2/n2=0.0206
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.012-0.0206)/sqrt((0.016*0.9841(1/11711+1/10360))
zo =-5.1434
| zo | =5.1434
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =5.143 & | z | =1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -5.1434 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: -5.1434
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0

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