Lesson 9 - Hypothesis Testing

Hypothesis Testing

A statistical inference method used to evaluate a conjecture about a characteristic of a population based on sample data.

Statistical Hypothesis

A claim about one or more populations that can be tested using sample data.

Null Hypothesis (Ho)

A statement assumed to be true until evidence indicates otherwise, often representing no effect or no difference.

Alternative Hypothesis (Ha)

A statement that contradicts the null hypothesis, representing what the researcher aims to prove.

One-Tailed Test

A hypothesis test where the alternative hypothesis specifies a direction of the difference or effect.

Two-Tailed Test

A hypothesis test where the alternative hypothesis does not specify a direction of the difference or effect.

Test Statistic

A value calculated from sample data used to determine whether to reject the null hypothesis.

Critical Region

The set of test statistic values that leads to the rejection of the null hypothesis.

Acceptance Region

The set of test statistic values that does not lead to the rejection of the null hypothesis.

Critical Value

A threshold that separates the critical region from the acceptance region in a hypothesis test.

Type I Error

Rejecting a true null hypothesis.

Type II Error

Failing to reject a false null hypothesis.

Level of Significance (α)

The maximum probability of committing a Type I error, often set at 0.01, 0.05, or 0.1.

P-value

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

Z-Test

A hypothesis test used when the population variance is known, and the sample size is large.

T-Test

A hypothesis test used when the population variance is unknown, particularly for small sample sizes.

Chi-Square Test

A test used to determine whether there is a significant association between categorical variables.

Paired Sample

A scenario in hypothesis testing where two related groups or measurements are compared.

Independent Sample

A scenario in hypothesis testing where two unrelated groups are compared.

Confidence Interval

A range of values derived from sample data that is likely to contain the true population parameter.

Expected Frequency

The frequency predicted under the null hypothesis in a contingency table.

Observed Frequency

The actual frequency recorded in a contingency table.

Degrees of Freedom

The number of independent values in a calculation, often used in determining critical values for tests.