Are you more likely to survive a heart attack during the day or during the night

Question

Are you more likely to survive a heart attack during the day or during the night? One theory is that the survival rate of heart attack victims will be lower at night because medical staffing is reduced. In a 2008 study printied in JAMA, this issue was explored by examining medical records over a 7-year period. The authors found that 11,604 of the 58,593 day-time patients survived, while 4,139 of the 28,155 night-time patients survived.

(a) What are the conditions necessary to do inference for two sample proportions? Given what you have been told, are they met in this setup?

(b) Construct a 97% CI for the difference in the true survival proportions.

(c) Run a hypothesis test using these data for the theory mentioned in the problem statement.

Explanation / Answer

a) The sampling method for each population is simple random sampling.
The samples are independent.
Each sample includes at least 10 successes and 10 failures.
Each population is at least 20 times as big as its sample.

Yes all the conditions are met

b) p1 = 11604/58593 = 0.198044, p2 = 4139/28155 = 0.147008
Critical z values = -/+1.8808
Standard error, se = sqrt[(p1(1-p1)/n1) + (p2(1-p2)/n2)] =  0.0026766

97% CI = (p1-p2) +/-zcrit*se = (11604/58593 - 4139/28155) +/- 1.8808*0.0026766 = (0.044084, 0.056071)

c) H0: P1 = P2
Ha: P1 > P2

Pooled sample proportion.p = (p1 * n1 + p2 * n2) / (n1 + n2) = 0.181480
Standard error.SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = 0.00279484

z = (p1 - p2) / SE = 18.26

p = 0

Reject null hypothesis, there is sufficient evidence to suggest the survival rate of heart attack vicitms is lower at night

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