ap stats

sampling distribution of p-hat

A list of all the possible values for p-hat together with the frequency (or probability) of each value; in other words, the distribution of all p-hat's from all possible samples.

Parameter

A number that describes a population.

Statisic

A number that describes a sample.

normal approximation for p-hat

A statistic of the data you are looking at (the parameter of interest; sample proportion)

Unbiased Estimator

If the mean of the sampling distribution is equal to the value of the parameter being estimated.

Normal condition of sample means

If the population distribution is Normal, then so is the sampling distribution of x-bar. This is true no matter what the sample size n is.

mean of the sampling distribution of x-bar (mean of sample)

The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

sampling distribution of x-bar (mean of sample)

The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

Sampling Distribution

The distribution of vales taken by the statistic in all possible samples of the same size from the same population (the ideal pattern that would emerge from a ton of samples).

Central Limit Theorem

The further the population is from being normally distributed, the larger the sample size needed for the distribution x-bar to be close to normal.

Sampling Variability

The idea that the value of a statistic varies in repeated sampling.

standard deviation of sampling distribution of p-hat

The standard deviation of (p) hat gets smaller as the sample size n increases because n appears in the denominator of the formula for the standard deviation.

standard deviation of the sampling distribution of x-bar (mean of sample)

The standard deviation of the sampling distribution of x-bar for an SRS of size n if the population has standard deviation σ. That is, averages are less variable than individual observations. This formula can be used if the population is at least 10 times as large as the sample (10% condition).

Population Distribution

a form of probability distribution that measures the frequency with which the items or variables that make up the population are drawn or expected to be drawn for a given research study.

variability of a statistic

described by the spread of its sampling distribution, this spread is determined by the sampling design and the size of the sample. Larger samples give smaller spread.

mean of the sampling distribution of p-hat

mean of p hat = p