Sampling Distributions

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 shape of the population distribution.

Front

What is the formula for the standard error of the mean (SEM)?

Back

SEM = σ / √n, where σ is the population standard deviation and n is the sample size.

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 relationship between the population standard deviation and the standard deviation of the sampling distribution?

Back

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

Front

What does it mean if a sampling distribution is approximately normal?

Back

It means that the distribution of sample means will form a bell-shaped curve, centered around the population mean, as the sample size increases.

Front

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

Back

The mean of the sampling distribution is equal to the mean of the population from which the samples are drawn.

Front

What is the standard error of the difference between two sample means?

Back

The standard error of the difference is calculated using the formula: SE_diff = √(SE1² + SE2²), where SE1 and SE2 are the standard errors of the two samples.

Front

How do you calculate the probability of a sample mean being greater than a certain value?

Back

To calculate this probability, use the z-score formula: z = (X - μ) / (σ/√n), then refer to the standard normal distribution table.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated as z = (X - μ) / σ.