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What sample size is needed to give a margin of error within +-2.5 in estimating a...

What sample size is needed to give a margin of error within +-2.5 in estimating a population mean with 95% confidence, assuming a previous sample had s=3.7

Round to nearest whole integer.

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Answer #1

Given that margin of error within E = +-2.5 in estimating a population mean with 95% confidence, assuming a previous sample had standard deviation, s=3.7.

The margin of error is calculated as:

Where Zc is the critical Z-score at the given confidence level, which is calculated using the excel formula for normal distribution which is =NORM.S.DIST(0.975) this results in Zc = 1.96

Now based on the margin of error formula the minimum sample is calculated as:

So, the minimum sample size is calculated as 8.

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