Unit 5: Sampling Distributions (copy)

Normal Distribution

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

Z-score

A measure of how many standard deviations an element is from the mean.

normalcdf

A function on the TI-84 calculator used to find the area (probability) under the normal curve between two z-scores or raw scores.

invNorm

A function on the TI-84 calculator that finds the z-score that corresponds to a given area (probability) to the left.

Central Limit Theorem (CLT)

States that the sampling distribution of the sample means approaches a normal distribution as the sample size becomes larger.

Bias

The systematic error introduced in a sampling process that causes the sample to differ from the population.

Unbiased Estimator

An estimator that is centered around the population parameter it is estimating.

Sampling Distribution

The probability distribution of a given sample statistic based on a random sample.

Mean (µ)

The average value of a set of data points in a population.

Standard Deviation (σ)

A measure of the amount of variation or dispersion in a set of values.

Sample Size (n)

The number of observations in a sample.

Probability of an Outcome

The likelihood that a specific outcome will occur in a probability distribution.

Sample Mean (x̄)

The average of a set of sample observations.

Parameter

A value that summarizes a characteristic of a population.

Qualitative Calculation

An assessment based on qualities or characteristics rather than quantities.

Normal Distribution of Sample Means

Indicates that the mean of a set of sample means is approximately normally distributed regardless of the shape of the population distribution.

Probability Distribution

A function that describes the likelihood of obtaining the possible values that a random variable can take.

Variance

A measure of how far a set of numbers are spread out from their average value.

Hypothesis Testing

A statistical method used to make decisions based on the results of data analysis.

Confidence Interval

A range of values derived from a data set that is likely to contain the value of an unknown population parameter.

Estimation

The process of inferring the value of a population parameter based on sample data.