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 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 the population mean is 400 and the population standard deviation is 40, what is the mean of the sampling distribution for a sample size of 25?

Back

The mean of the sampling distribution is equal to the population mean, which is 400.

Front

What happens to the standard error as the sample size increases?

Back

As the sample size increases, the standard error decreases.

Front

Define 'sampling distribution'.

Back

A sampling distribution is the probability distribution of a statistic (like the mean) obtained from a large number of samples drawn from a specific population.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean of the population.

Front

How does the shape of the sampling distribution change as the sample size increases?

Back

The shape becomes narrower and more normal as the sample size increases.

Front

What is the relationship between the population standard deviation and the standard error?

Back

The standard error is the population standard deviation divided by the square root of the sample size.

Front

What does a z-score of -0.3 represent in terms of area under the curve?

Back

A z-score of -0.3 corresponds to an area of approximately 0.3821 to the left of the z-score in a standard normal distribution.

Front

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

Back

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