A study in the New England Journal of Medicine reported that based on 987 deaths
ID: 3313161 • Letter: A
Question
A study in the New England Journal of Medicine reported that based on 987 deaths in southern California, right-handers died at an average age of 75 and left-handers died at an average age of 66. In addition, it was found that 7.9% of the lefties died from accident-related injuries, excluding vehicles, versus 1.5% for the right-handers, and 5.3% of the left-handers died while driving vehicles versus 1.4% of the right-handers. Suppose you examine 1000 randomly selected death certificates, of which 100 were left-handers and 900 were right-handers. If you found that 5 of the left-handers and 18 of the right-handers died while driving a vehicle, would you have evidence to show that the proportion of left-handers who die at the wheel is significantly higher than the proportion of right-handers who die while driving? Calculate the p-value and interpret its meaning.Explanation / Answer
The test for two proportions can be used denoting p1 and p2 as the proportiin of drivers who die at wheel for right and left handers respectively. Here p1=18/900 and p2=5/100.The variances are n*p*(1-p). The statistic thus becomes
(p1-p2) /sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)
We will compare that with the critical value of either 1.96 or - 1.96 for a 95% confidence interval. If it exceeds in either direction then null hypothesis is rejected and we can conclude that left handers have high probability of dying.
The hypothesis is H0:p1=p2 H1:p2>p1
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