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The minimum sample size required to estimate a population mean with a confidence of 95%, a margin error of 2 units and a standard deviation of 10 units is 96.
A minimum sample size is the number of participants one needs to maintain their target confidence interval (margin of error) and confidence level while obtaining results that accurately represent the population they are studying.
The formula to calculate the minimum sample size for the population mean is [tex]\bold{n=\left(\frac{z\times \sigma}{E}\right)^2}[/tex]. Here, n is the sample size, z is the confidence level, σ is the standard deviation, and E is the margin error.
Given, the z-value for 95% confidence is 1.96, E is 2 and σ is 10.
Then, the minimum sample size is,
[tex]\begin{aligned}n&=\left(\frac{1.96\times10}{2}\right)^2\\&=(9.8)^2\\&=96.04\\&\approx96\end{aligned}[/tex]
The answer is 96.
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