Probability and Sampling Distributions

frequentist probability

probability of any event A is the ratio of the number of times the event happens divided by the number of times any event happens

probability density functions

show more fine-grained probabilities than a histogram can show; curves -> theoretical distributions of statistics

normal (no skew)

right/positive skewed

left/negative skewed

normal distributions of populations

N(µ, σ²)

standardizing a normal distribution

effect of larger samples on sampling distribution of means

less variable means

mean of sampling distribution of means

equal to the population mean

standard error of sampling distribution of means

unbiased estimator

when the mean of a statistic across all samples of the same size equals the value of the parameter

central limit theorem

sampling distribution of sample means approaches normality even from non-normal populations, with large enough sample sizes

what does CLT allow us to do with statistical tests?

allows us to use a normal sampling distribution when calculating probabilities (to infer about population means)