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.

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Quizplus · Accepted Answer

The standard error of the sampling distribution of the sample mean difference is calculated using the formula $\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$. For the given variances and sample sizes, it is $\sqrt{\frac{25}{36} + \frac{16}{36}} = \sqrt{\frac{41}{36}} \approx 1.07$, not 5.

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