Sampling Distributions Review

Front

What is a sampling distribution?

Back

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

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large, regardless of the population's distribution.

Front

What is the mean of the sampling distribution of the sample mean?

Back

The mean of the sampling distribution of the sample mean is equal to the population mean (μ).

Front

What is the standard deviation of the sampling distribution of the sample mean?

Back

The standard deviation of the sampling distribution of the sample mean is called the standard error and is calculated as σ/√n, where σ is the population standard deviation and n is the sample size.

Front

What happens to the standard error as the sample size increases?

Back

As the sample size increases, the standard error decreases, meaning the sampling distribution becomes narrower.

Front

What is the relationship between sample size and the accuracy of the sample mean?

Back

Larger sample sizes generally lead to more accurate estimates of the population mean.

Front

What is the difference between a population and a sample?

Back

A population includes all members of a specified group, while a sample is a subset of the population used to make inferences about the population.

Front

What does it mean if a sampling distribution is normal?

Back

If a sampling distribution is normal, it means that the distribution of the sample means forms a bell-shaped curve, indicating that most sample means are close to the population mean.

Front

How do you calculate the standard error for a sample size of 25 with a population standard deviation of 40?

Back

Standard error = σ/√n = 40/√25 = 40/5 = 8.

Front

What is the significance of the sample mean being equal to the population mean?

Back

It indicates that the sample mean is an unbiased estimator of the population mean.