Central Limit Theorem

Front

What does the Central Limit Theorem state?

Back

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

Front

What is the mean of the sampling distribution?

Back

The mean of the sampling distribution is equal to the mean of the population.

Front

What is the standard error of the mean?

Back

The standard error of the mean is the standard deviation of the sampling distribution, calculated as the population standard deviation divided by the square root of the sample size.

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 is the significance of a sample size of 30 in the Central Limit Theorem?

Back

A sample size of 30 is often considered sufficient for the Central Limit Theorem to hold, meaning the sampling distribution of the sample mean will be approximately normal.

Front

What is the relationship between population distribution and sampling distribution according to the Central Limit Theorem?

Back

The Central Limit Theorem indicates that regardless of the population distribution, the sampling distribution of the sample mean will be approximately normal if the sample size is large enough.

Front

What is the difference between population standard deviation and sample standard deviation?

Back

Population standard deviation (σ) is used when considering the entire population, while sample standard deviation (s) is used when considering a sample from the population.

Front

How do you determine if the Central Limit Theorem applies?

Back

The Central Limit Theorem applies if the sample size is large (typically n ≥ 30) or if the population distribution is normal.

Front

What is the probability of a sample mean being greater than a certain value?

Back

To find this probability, you can use the Z-score formula: Z = (X̄ - μ) / (σ/√n), where X̄ is the sample mean, μ is the population mean, and σ is the population standard deviation.

Front

What does it mean if a sample mean is within one standard error of the population mean?

Back

If a sample mean is within one standard error of the population mean, it indicates that the sample mean is likely to be a good estimate of the population mean.