Probability and Samples: The Distribution of Sample Means

Flashcards covering key vocabulary related to the distribution of sample means, sampling error, and the Central Limit Theorem.

Distribution of Sample Means

The collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.

Sampling Distribution

A distribution of statistics obtained by selecting all the possible samples of a specific size from a population.

Sampling Error

The natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.

Central Limit Theorem

For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will have a mean of μ and a standard deviation of s/n and will approach a normal distribution as n approaches infinity.

Expected Value of M

The mean of the distribution of sample means, which is equal to the population mean (μ).

Standard Error of M (σM)

The standard deviation of the distribution of sample means and measures the standard distance between a sample mean and the population mean, calculated as σ/n.

Law of Large Numbers

States that the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.

Conditions for a Normal Distribution of Sample Means

The distribution is almost perfectly normal if the population from which samples are selected is normal, or if the number of scores (n) in each sample is relatively large (around 30 or more).

Z-score for a Sample Mean

A value that specifies the location of a sample mean within the distribution of sample means, calculated as (M - μ) / σM.