Significance Tests for a Population Mean (Module 6)

These flashcards cover key vocabulary and concepts related to significance tests for population means, as outlined in the lecture notes.

Hypothesis

A statement or assumption about a population parameter that can be tested using sample data.

Null Hypothesis (H0)

The claim that there is no effect, no difference, or status quo.

Alternative Hypothesis (H1 or Ha)

The claim that there is an effect or difference.

One-Tailed Test

A hypothesis test that tests for the possibility of the relationship in one direction only (either greater than or less than).

Two-Tailed Test

A hypothesis test that tests for the possibility of the relationship in both directions (higher or lower).

Test Statistic

A standardized value that measures how far the sample result is from the hypothesized population value.

Rejection Region

The range of values that are too extreme to be consistent with the null hypothesis, leading to its rejection.

Significance Level (α)

The probability of rejecting the null hypothesis when it is actually true, also known as the risk of a Type I error.

Type I Error

Rejecting a true null hypothesis.

Type II Error

Failing to reject a false null hypothesis.

p-value

The probability of obtaining a test statistic as extreme as or more extreme than the one observed, under the assumption that the null hypothesis is true.

One-Sample z-Test

A test used when the population standard deviation is known and the sample size is large, to compare a sample mean to a hypothesized population mean.

One-Sample t-Test

A test used when the population standard deviation is unknown and the sample size is small or large, to compare a sample mean to a hypothesized population mean.

Degrees of Freedom (df)

The number of independent values or quantities which can be assigned to a statistical distribution.

Central Limit Theorem (CLT)

The theorem that states that the distribution of the sample mean approaches a normal distribution as the sample size becomes larger, regardless of the population's distribution.