The Central Limit Theorem - MATH 170 Notes Summary

Flashcards summarizing key concepts from MATH 170 lecture notes on the Central Limit Theorem.

Rounding Error

Avoiding rounding at intermediate calculations, rounding to at least six decimal places to minimize errors.

Sampling Distribution

The probability distribution of a sample statistic for all possible samples of size n.

Expected Value of Sample Mean

The population mean, denoted by µ.

Central Limit Theorem (CLT)

As sample size increases, the shape of the sampling distribution of sample means approaches a normal distribution.

Standard Error of the Mean

The standard deviation of the sampling distribution of sample means, denoted as σx̄ = σ/√n.

Sample Proportion

The fraction of a sample that has a certain characteristic, denoted as ˆp.

Population Proportion

The fraction or percentage of the population with a certain characteristic, denoted as p.

Normal Approximation

Applicable for sampling distributions if either sample size n ≥ 30 or the population is normally distributed.

Standard Score (z-score)

Calculated as z = (x̄ - µ)/σx̄ for sample means.

Binomial Distribution

The distribution for sampling proportions when conditions np ≥ 10 and n(1-p) ≥ 10 are met.