Central Limit Theorem Notes

Flashcards based on the concepts from the lecture notes about the Central Limit Theorem, sampling distribution, and related statistical methods.

Central Limit Theorem

States that the sampling distribution of the mean approaches a normal distribution as the sample size increases.

Sampling Distribution

The probability distribution of a statistic for a large number of samples taken from a population.

Standard Error of the Mean (SEM)

Measures the degree of accuracy of the sample mean as an estimate of the population mean.

Formula for Z-Score

Z = (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Population Standard Deviation

A measure of the dispersion of a set of values; denoted by σ.

Good Estimate of the Mean

Occurs when the sample size is large enough to provide an accurate reflection of the population mean.

Normal Distribution

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence.

Probability of Sample Mean

The likelihood that the sample mean will lie within a specific range; calculated using z-scores and standard error.

Z-Table

A mathematical table used to calculate the area under the normal curve corresponding to the z-score.

Sample Size (n)

The number of observations in a sample, which affects the accuracy of the sample mean as an estimate.