You take and SRS of size 25 from a population with mean 200 and standard deviation of 10. Find the mean and the standard deviation of the sampling distribution of your sample mean.

I would predict the same mean.

Standard deviation/error of the mean (SEm) = SD/√(n-1)

To find the mean of the sampling distribution of the sample mean, we use the fact that the mean of the sampling distribution is equal to the mean of the population. In this case, the population mean is 200.

Therefore, the mean of the sampling distribution of the sample mean is 200.

To find the standard deviation of the sampling distribution of the sample mean, we use the formula:

Standard deviation of the sampling distribution = (Standard deviation of the population) / √(sample size)

In this case, the standard deviation of the population is 10 and the sample size is 25.

Plugging these values into the formula, we get:

Standard deviation of the sampling distribution = 10 / √(25)

Standard deviation of the sampling distribution = 10 / 5

Standard deviation of the sampling distribution = 2

Therefore, the standard deviation of the sampling distribution of the sample mean is 2.

To find the mean and standard deviation of the sampling distribution of the sample mean, we can use the following formulas:

Mean of sampling distribution of the sample mean (μᵢ):
The mean of the sampling distribution of the sample mean is equal to the mean of the population, which in this case is given as 200.

Standard deviation of the sampling distribution of the sample mean (σᵢ):
The standard deviation of the sampling distribution of the sample mean is calculated using the formula:

σᵢ = σ / √(n)

where σ is the standard deviation of the population, and n is the sample size.

In this case, the standard deviation of the population is given as 10, and the sample size is 25. Plugging these values into the formula, we get:

σᵢ = 10 / √(25) = 10 / 5 = 2

So, the mean of the sampling distribution of the sample mean is 200, and the standard deviation is 2.