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. 2011 May 10;469(9):2661–2664. doi: 10.1007/s11999-011-1908-9

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Fig. 2 — The cascade from the distribution of the parameter in the population, to the sampling distribution of the means, and to a single sample is shown. We can see how we work our way back from the mean and standard error of the mean in the sample (m₁ = 7.4, and se = 0.57), to construct an interval (m₁ ± 1.96 × se), closely resembling the interval ± 1.96 × sd_m, that has a 95% probability to include the true population mean (μ = 8).

Inline graphic — The cascade from the distribution of the parameter in the population, to the sampling distribution of the means, and to a single sample is shown. We can see how we work our way back from the mean and standard error of the mean in the sample (m₁ = 7.4, and se = 0.57), to construct an interval (m₁ ± 1.96 × se), closely resembling the interval ± 1.96 × sd_m, that has a 95% probability to include the true population mean (μ = 8).