5.4 Central Limit Theorem

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the distribution of the sample means will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution, provided the sample size is sufficiently large (usually n ≥ 30).

Front

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

Back

The mean of the sampling distribution of the sample means is equal to the mean of the population from which the samples are drawn, denoted as @@ u@@.

Front

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

Back

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

Back

A sample size of 30 is often considered the minimum size for the Central Limit Theorem to hold true, allowing the sampling distribution of the mean to approximate a normal distribution.

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 does it mean for a sample mean to be considered unusual?

Back

A sample mean is considered unusual if it lies more than 2 standard deviations away from the population mean, indicating it is unlikely to occur under normal circumstances.

Front

How do you calculate the probability of a sample mean?

Back

Front

What is the relationship between population distribution and sampling distribution?

Back

The shape of the population distribution affects the shape of the sampling distribution, but as sample size increases, the sampling distribution will tend to be normal regardless of the population's shape.

Front

What is the formula for the z-score in the context of the Central Limit Theorem?

Back

The z-score formula is @@z = rac{ar{x} - u}{rac{ ext{population standard deviation}}{ ext{sqrt(n)}}}@@.