Question

In the 1980’s, a clinical trial was conducted to determine if taking an aspirin daily reduced the incidence of heart attacks. Of 22,071 medical doctors participating in the study, 11,037 were randomly assigned to take aspirin and 11,034 were randomly assigned to the placebo group. Doctors in this group were given a sugar pill disguised to look like aspirin. After six months, the proportion of heart attacks in the two groups was compared. Only 104 doctors who took aspirin had a heart attack, whereas 189 who received the placebo had a heart attack. Can we conclude from this study that taking aspirin reduced the chance of having a heart attack? the purpose of this study was to determine whether taking an aspirin daily reduces the proportion of heart attacks.

Answer 1

There is enough evidence to conclude that taking aspirin cannot  reduces the chance of cancer.

Given sample size of patients take aspirin 11037, sample size of patients who have assigned placebo group be 11034. 104 doctors who take aspirin had a heart attack, 189 doctors had placebo had heart attacks.

First we have to form hypothesis.

$H_{0} :p{1} -p_{2} =0$

$H_{1}:p_{1} -p_{2} < 0$

We have to find the respective probabilities.

$p_{1}$=104/11037

=0.0094

$p_{2}$=189/11034

=0.0171

Now their respective margin of errors.

$s_{1}$=$\sqrt{ {(0.0094*0.9906)/11037}$

=0.0009

$s_{2}$=$\sqrt{0.0171*0.9829}$

=0.0011

Hence the distribution of the differences,they are given by:

p=$p_{1} -p_{2}$

=0.0094-0.0171

=-0.0077

S=$\sqrt{s_{1} ^{2}+s_{2} ^{2} }$

=$\sqrt{(0.0009)^{2} +(0.0011)^{2} }$

=0.00305

z=(p -f)/S (In which f=0 is the value tested at the null hypothesis)

=(-0.0077-0)/0.00305

=-2.52

p value will be 0.005.

p value of 0.05 significance level.

z=1.96.

1.96>0.005

So we will reject the null hypothesis which means it cannot reduce the whole chance of becomming a heart attack.

Hence there is enough evidence to conclude that taking aspirin cannot  reduces the chance of cancer.

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