Statistical Inference Flashcards

Collection of key terms and definitions related to statistical inference, hypothesis testing, and statistical methods.

Population

A well-defined collection of objects pertaining to a phenomenon of statistical inquiry.

Sample

A small part or subset of a population used for statistical inquiry.

Finite Population

When the number of units under investigation is finite and determinable.

Infinite Population

When the number of units under investigation is infinite and indeterminable.

Statistical Inference

The process of making inferences about a population based on samples taken from it.

Parameter

Any measure calculated on the basis of population values, such as population mean, standard deviation, etc.

Statistic

Any quantity whose value can be calculated from sample data; considered a random variable.

Sampling Distribution

The probability distribution of a statistic.

Random Sample

A sample of size n formed by independent random variables with the same probability distribution.

Central Limit Theorem (CLT)

States that the sample mean will have an approximately normal distribution if the sample size is large enough.

Sample Mean

The average of a sample, denoted as X̄.

Confidence Interval (CI)

An interval estimate within which a population parameter is expected to fall with a certain level of confidence.

Null Hypothesis (Ho)

The claim that is initially assumed to be true in hypothesis testing.

Alternative Hypothesis (Ha)

The assertion that contradicts the null hypothesis.

Type I Error

Rejecting the null hypothesis when it is actually true.

Type II Error

Failing to reject the null hypothesis when it is actually false.

Test Statistic

A function of the sample data used to decide whether to reject the null hypothesis.

Rejection Region

The set of all test statistic values for which the null hypothesis will be rejected.

One-tailed Test

A hypothesis test in which the rejection region is located at one end of the distribution.

Two-tailed Test

A hypothesis test in which the rejection region is located at both ends of the distribution.

P-value

The probability of observing the test results under the null hypothesis.

Significance Level (α)

The probability of making a Type I error, typically set at 0.05, 0.01, or 0.10.

Power of a Test

The probability of correctly rejecting the null hypothesis when it is false.