Check for Understanding - Sampling Distributions

Front

What is a sampling distribution?

Back

A sampling distribution is the probability distribution of a statistic (like the mean) obtained from a large number of samples drawn from a specific population.

Front

What is the standard deviation of the sampling distribution (also known as the standard error)?

Back

The standard deviation of the sampling distribution is calculated as the population standard deviation divided by the square root of the sample size (σ/√n).

Front

If the population mean is 200, what is the mean of the sampling distribution?

Back

The mean of the sampling distribution is equal to the population mean, which is 200.

Front

What is the formula for calculating the standard error?

Back

Standard Error (SE) = σ / √n, where σ is the population standard deviation and n is the sample size.

Front

What does a smaller standard error indicate about the sampling distribution?

Back

A smaller standard error indicates that the sample means are closer to the population mean, suggesting less variability.

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Front

How does sample size affect the standard error?

Back

As the sample size increases, the standard error decreases, leading to a more precise estimate of the population mean.

Front

What is the probability of selecting a sample mean less than a certain value?

Back

To find this probability, you can use the Z-score formula and the standard normal distribution.

Front

What is the significance of a Z-score in sampling distributions?

Back

A Z-score indicates how many standard deviations an element is from the mean, helping to determine probabilities in a normal distribution.

Front

What is the relationship between population standard deviation and sampling distribution standard deviation?

Back

The standard deviation of the sampling distribution (standard error) is the population standard deviation divided by the square root of the sample size.