A clinical trial of n=600 infants using Drug A found that that 40% were cured of sepsis. What is the 98% confidence interval for the drug's effectiveness? A previous study showed that the proportion of subjects cured under a placebo is 36%. Based on the answer from (a) is there enough evidence to suggest that Drug A is significantly better than a placebo?
sample size, n=600 sample proportion, p = 0.4 we use normal approximation, for this we check that both np and n(1-p) > 5. Since n*p = 240 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.4 and std deviation = root( p * (1-p) /n ) = 0.02
For constructing Confidence interval, Margin of Error (ME) = z x SD = 0.0465
98% confidence interval is given by: Sample Mean +/- (Margin of Error) 0.4 +/- 0.0465 = (0.3535 , 0.4465)
We have n = 600, sample proportion p = 0.4 and P = 0.36 we want to test whether hypothesis: H0: true P <= 0.36 (null hypothesis) Ha: true P > 0.36 (alternative hypothesis)
now, calculating statistics, (test statistic) sigma s = sqrt(P*(1-P)/n) = 0.0196 z-score = (p-P)/s = 2.0408 this is right tailed test, hence p-value = P( z > 2.0408) = 0.0413
this is less than 0.05, so we reject null, and yes this is significantly beter
Apr 4th, 2015
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