Central Limit Theorem Concepts

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 of the sample means?

Back

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

Front

What happens to the standard deviation of the sampling distribution as sample size increases?

Back

The standard deviation of the sampling distribution (standard error) decreases as the sample size increases.

Front

Define standard error.

Back

Standard error is the standard deviation of the sampling distribution of a statistic, commonly the mean.

Front

What is the relationship between sample size and the shape of the sampling distribution?

Back

As the sample size increases, the shape of the sampling distribution becomes narrower and more normal.

Front

What is the formula for calculating the standard error of the mean?

Back

Standard Error (SE) = σ / √n, where σ is the population standard deviation and n is the sample size.

Front

If a population has a mean of 50 and a standard deviation of 10, what is the mean of the sampling distribution for a sample size of 36?

Back

The mean of the sampling distribution is 50.

Front

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

Back

To find this probability, use the Z-score formula and the standard normal distribution table.

Front

What does it mean if a sampling distribution is normally distributed?

Back

It means that the sample means are symmetrically distributed around the population mean, forming a bell-shaped curve.

Front

How does the Central Limit Theorem apply to non-normal populations?

Back

The Central Limit Theorem allows us to use normal distribution approximations for sample means even if the population distribution is not normal, provided the sample size is sufficiently large.