Central Limit Theorem

Front

What is the Central Limit Theorem?

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 if the population mean is 400?

Back

400

Front

What is the standard error of the sampling distribution if the population standard deviation is 40 and the sample size is 25?

Back

8

Front

True or False: The distribution of the sample means will become approximately normal if the sample size is increased, regardless of the population distribution.

Back

True

Front

What sample size is required for the Central Limit Theorem to hold if the original distribution is not normal?

Back

30

Front

What is the formula for calculating 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

If a population has a mean of 400 and a standard deviation of 40, what is the probability that the sample mean of a sample of size 25 falls between 390 and 410?

Back

Approximately 0.9545 (using the normal distribution).

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.

Front

How does increasing the sample size affect the standard error?

Back

Increasing the sample size decreases the standard error, making the sampling distribution narrower.

Front

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

Back

The sampling distribution of the sample means will be approximately normal if the sample size is sufficiently large, regardless of the population distribution.