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Alternatively, let's say you are reporting to your boss on the results of a new procedure...

Alternatively, 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?

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