Questions: The mean of the sampling distribution of (barx1-barx2) is always 0 (Zero). always positive. always (mu 1-mu 2). always negative.

Transcript text: The mean of the sampling distribution of $\bar{x}_{1}-\bar{x}_{2}$ is always 0 (Zero). always positive. always $\mu 1-\mu 2$. always negative.

Solution

Solution Steps

To determine the mean of the sampling distribution of the difference between two sample means, we use the properties of expected values. The mean of the sampling distribution of $\bar{x}_{1} - \bar{x}_{2}$ is equal to the difference between the means of the two populations, $\mu_1 - \mu_2$.

Step 1: Understanding the Problem

We need to find the mean of the sampling distribution of the difference between two sample means, $\bar{x}_{1} - \bar{x}_{2}$. According to statistical theory, this mean is equal to the difference between the means of the two populations, $\mu_1 - \mu_2$.

Step 2: Given Values

We are given the means of two populations:

$\mu_1 = 10$
$\mu_2 = 5$

Step 3: Calculate the Mean of the Sampling Distribution

The mean of the sampling distribution of $\bar{x}_{1} - \bar{x}_{2}$ is calculated as: \[ \mu_{\bar{x}_{1} - \bar{x}_{2}} = \mu_1 - \mu_2 \] Substituting the given values: \[ \mu_{\bar{x}_{1} - \bar{x}_{2}} = 10 - 5 = 5 \]