Sampling Distribution

Flashcards cover key concepts of sampling distributions, including definitions and critical points regarding sample means, standard errors, and the effects of population characteristics.

Sampling distribution

The distribution of all possible values of a sample statistic for a given sample size selected from a population.

Population mean

The average of all the values in a population.

Sample statistic mean

The mean calculated from a sample that estimates the population mean.

Standard error

The standard deviation of the sampling distribution, which quantifies the accuracy of the sample statistic as an estimate of the population parameter.

Standard deviation vs. Standard error

Standard error is always less than the population standard deviation.

Mean of sample means

The mean of the sample means is always equal to the population mean.

Standard error formula

The standard error of the sample mean is equal to the population standard deviation divided by the square root of the sample size.

Normal distribution

A probability distribution that is symmetric and characterized by its mean and standard deviation.

Central Limit Theorem

States that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is large enough.

Sample size criteria for CLT

The Central Limit Theorem applies if the sample size is at least 30.

Sampling distribution of proportions

The distribution of the sample proportion, which estimates the population proportion.

Population proportion (π)

The true proportion of a characteristic in the population.

Sample proportion (p)

The proportion calculated from the sample, estimating the population proportion.

Standard error of the sample proportion

The standard deviation of the sampling distribution of the sample proportion.

Binomial distribution

A discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials.

Finite population correction (FPC)

A factor used to reduce the standard error when sampling without replacement from finite populations.

Standard error of the mean for finite populations

Adjusted standard error for situations where samples are drawn from finite populations.

Standard error of the proportion for finite populations

The standard error of the sample proportion adjusted for finite populations.

Z-score

A statistical measurement that describes a value's relation to the mean of a group of values.

Observational uncertainty

The uncertainty in a sample statistic that arises from not knowing certain observations.

Increasing accuracy of estimators

Reducing standard error leads to improved accuracy in estimating population parameters.

Size of the population

The total number of individuals or items that constitute the population.

Sample size influence

Larger sample sizes reduce the uncertainty related to the sample statistic.

Approximate normal distribution for proportions

Occurs when sample size is large enough under certain conditions.

Characteristics of Normal populations

If the population is normally distributed, the sample mean will also be normally distributed.