Sampling Distribution Sample Means

What happens to the shape of a sampling distribution of sample means as the sample size (n) increases?

• It becomes narrower (less variability) and bimodal.

• It becomes narrower (less variability) and more normal.

• It becomes wider (more variability) and skewed right.

• It becomes wider (more variability) and more normal.

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

The mean of the sampling distribution is the same as the mean of the population.

• True

• False

The standard deviation of a sampling distribution is the same as the standard deviation as the population.

• True

• False

The mean of a population is μ = 200 the standard deviation is σ = 20. Random samples of size 25 are taken from this population.

What is the mean of the sampling distribution?

• 200

• 16

• 25

• 4

The mean of a population is μ = 200 the standard deviation is σ = 20. Random samples of size 25 are taken from this population.

What is the standard deviation of the sampling distribution?

• 200

• 16

• 25

• 4

If $\mu\ =\ 100$  and  $\sigma\ =\ 15$  and repeated samples of size 10 are taken, what are the mean and standard deviation of the sampling distribution?

•  $\mu_x=\ 100$  and  $\sigma_x\ =\ 15$  

•  $\mu_x=\ 100$  and  $\sigma_{\ x}\ =\ \frac{\sqrt{15}}{10}$  

•  $\mu_x=\ 100$  and  $\sigma_{x\ }=\frac{15}{\sqrt{10}}$  

•  $\mu_{x\ }=\ \frac{15}{\sqrt{10}}$  and  $\sigma_{x\ }=\ 100$  

Consider a population with  $\mu=50$  and  $\sigma=5$ is taken. Find the mean of the sampling distribution of the sample mean with a sample size of 30.

• 50

• 25

• 20

• 5