Sampling Distributions #1: Quigley

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 is the Central Limit Theorem?

Back

The Central Limit Theorem states that the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, as long as the sample size is sufficiently large (usually n ≥ 30).

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How do you calculate the standard deviation of a sampling distribution?

Back

The standard deviation of a sampling distribution (also known as the standard error) is calculated using the formula: SE = σ / √n, where σ is the population standard deviation and n is the sample size.

Front

If the population mean is 200 and the population standard deviation is 20, what is the standard deviation of the sampling distribution for a sample size of 25?

Back

The standard deviation of the sampling distribution is 4.

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What is the formula for calculating the z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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What does a z-score represent in a sampling distribution?

Back

A z-score represents the number of standard deviations a data point is from the mean of the sampling distribution.

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How do you find the probability of a sample mean being less than a certain value?

Back

To find the probability of a sample mean being less than a certain value, calculate the z-score for that value and then use the standard normal distribution table to find the corresponding probability.

Tags

CCSS.HSS.ID.A.4

Front

What is the significance of a sample size of 40 in probability calculations?

Back

A sample size of 40 is often considered large enough for the Central Limit Theorem to apply, allowing the sampling distribution of the sample mean to be approximately normal.

Front

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

Back

To find this probability, calculate the z-score for that value and then subtract the corresponding probability from 1.

Tags

CCSS.HSS.ID.A.4

Front

What is the standard error of the mean?

Back

The standard error of the mean is the standard deviation of the sampling distribution of the sample mean, indicating how much the sample mean is expected to vary from the population mean.