The standard error of difference of two large (independent) sample means is .

Question

Quizplus · Accepted Answer

The standard error of difference of two large (independent) sample means can be estimated using the formula:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

where s1 and s2 are the standard deviations of the two samples and n1 and n2 are the sample sizes. When the sample sizes are large (generally n1 ≥ 30 and n2 ≥ 30), the central limit theorem applies and the distribution of the sample means is approximately normal. Therefore, the standard error of the difference of means is a valid measure of how much the sample means vary from the true population means. The standard error of difference of two large (independent) sample means can be calculated using the formula SE = sqrt[(s1^2/n1) + (s2^2/n2)] where s1 and s2 are the standard deviations of the two samples and n1 and n2 are the sample sizes. This formula holds true for large sample sizes (typically n1 and n2 > 30), and assumes that the population variances are equal. If the sample sizes are small, or if the population variances are unknown or unequal, then other methods like the t-test or the Welch's t-test may be used to calculate the standard error.

The Standard Error of Difference of Two Large (Independent) Sample