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7. Which study will require a larger sample size, one done with 80% power or 90%...

7. Which study will require a larger sample size, one done with 80% power or 90% power when alpha (type I error) is set at 0.05 and we use the same population and expected difference and variation for both studies?

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Answer #1

Formula for sample size is given as

where is the z critical value corresponding to the power level

for 80% power is 0.84 and for 90% power is 1.282

So, it is clear that the is higher for 90% power.

From the formula, it is clear that the sample size varies directly with

Higher value of corresponds to larger sample size and lower value of corresponds to smaller sample size

therefore, 90% power will require a larger sample size

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