Suppose that $x$ is a normally distributed variable on each of two populations. Independent samples of sizes $n _ { 1 }$ and $n _ { 2 }$, respectively, are selected from the two populations.The standard deviation of all possible differences between the two sample means equals the square root of the difference of the population variances each divided by the corresponding sample size.

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The standard deviation of all possible differences between two sample means (also known as the standard error of the difference between two means) equals the square root of the sum (not the difference) of the population variances each divided by the corresponding sample size. The formula is $\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$, where $\sigma_1^2$ and $\sigma_2^2$ are the population variances, and $n_1$ and $n_2$ are the sample sizes.

Suppose That xxx Is a Normally Distributed Variable on Each of Two Populations

Suppose That $x$ Is a Normally Distributed Variable on Each of Two Populations