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Analyzing Sample Means and Their Plausible Values with Distance from the Mean

This analysis explores the plausible values of sample means calculated at various distances from the mean (m) of a distribution. Specifically, we examine scenarios where m equals 0.25, 0.10, 0, -0.10, and -0.20, with accompanying standard deviations (SDs) representing distances from the mean being 2.05, 0.46, 0.59, 1.65, and a general statistic of 2.70 SDs away. Each scenario helps in understanding how changes in the mean affect the sample distributions, which can inform statistical decision-making processes.

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Analyzing Sample Means and Their Plausible Values with Distance from the Mean

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  1. Observed sample mean Plausible values of m Suppose m=.25 2.05 SDs away Suppose m=.10 .46 SDs away Suppose m=0 .59 SDs away Suppose m=-.10 1.65 SDs away Suppose m=-.20  Sample means  2.70 SDs away ( )

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