If two random samples of size 36 each are selected independently from two populations with variances 25 and 16, then the standard error of the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , is 5-4 = 1.

Question

Quizplus · Accepted Answer

The standard error of the difference between two sample means is calculated using the formula $\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$, which in this case is $\sqrt{\frac{25}{36} + \frac{16}{36}}$, not simply 5 - 4.

If Two Random Samples of Size 36 Each Are Selected Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​

If Two Random Samples of Size 36 Each Are Selected $\bar { X } _ { 1 } - \bar { X } _ { 2 }$