Hoping someone can walk me through this - step by step: Let\'s say you are repor

Question

Hoping someone can walk me through this - step by step:

Let's say you are reporting to your boss on the results of a new procedure to save the world.   As evidence, you have a sample from the old procedure that says it saves 67 lives on average, with a standard error of 1.5 lives (not margin of error). A sample with the new procedure saves 72.5 lives, and also has a standard error of 1.5 lives.   What can you tell your boss?   Is the new procedure effective at a 95% confidence level?   What would be the next step?   Would you answer differently if the sample size were 36 versus 100?

Explanation / Answer

follwoing information has been given

we use z-test for difference to sample means with

null hypothesis H0: old (mean)=new (mean)

alternate hypothesis H1: old(mean)<new( mean)

and statistic z=(new-old)/SE(new-old)=(72.5-67)/2.12=2.59 is more than one tailed critical z(0.05)=1.645

so we fail to accept H0 and conclude that new procedure is effective.

SE(new - old)=sqrt(SE(new)*SE(new)+SE(old)+SE(old))=sqrt(1.5*1.5+1.5*1.5)=2.12

since the standard error is the function of sample size i,e. SE=sd/sqrt(n), so answer will be differently if the sample size 100.

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