Two samples are selected at random from two independent normally distributed populations. Sample 1 has 49 observations and has a mean of 10 and a standard deviation of 5. Sample 2 has 36 observations and has a mean of 12 and a standard deviation of 3. The standard error of the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , is:
A)0.1853.
B)0.7602.
C)0.7331.
D)0.8719.

Question

Quizplus · Accepted Answer

The standard error of the difference between two independent sample means is calculated using the formula: $\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$. Substituting the given values: $\sqrt{\frac{5^2}{49} + \frac{3^2}{36}} = \sqrt{\frac{25}{49} + \frac{9}{36}} = \sqrt{0.5102 + 0.25} = \sqrt{0.7602} = 0.8719$.

Two Samples Are Selected at Random from Two Independent Normally Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​

Two Samples Are Selected at Random from Two Independent Normally $\bar { X } _ { 1 } - \bar { X } _ { 2 }$