T-Distribution and Hypothesis Testing

Flashcards covering key terms and concepts related to the t-distribution and hypothesis testing.

T-distribution

A probability distribution that is symmetric and bell-shaped, used when the sample size is small and the population standard deviation is unknown.

Degrees of Freedom (df)

A parameter used in statistical tests that defines the number of independent values that can vary in an analysis without violating any constraints.

Null Hypothesis (H0)

A statement that there is no effect or no difference, and it is tested to determine whether it can be rejected.

Alternative Hypothesis (H1)

The hypothesis that suggests there is an effect or a difference, opposing the null hypothesis.

Type I Error

The error made when the null hypothesis is rejected when it is actually true.

Type II Error

The error that occurs when the null hypothesis is not rejected when it is false.

Significance Level (α)

The threshold at which the null hypothesis is rejected, commonly set at 0.05.

Power of a Test

The probability that a test will correctly reject a false null hypothesis.

Chi-Square Test (χ²)

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

F-distribution

A probability distribution used to compare two variances by analyzing the ratio of two sample variances.

Z-test

A statistical test used to determine whether there is a significant difference between the means of two groups, applicable when sample sizes are large enough or the population variance is known.

T-test

A statistical test used to determine whether there is a significant difference between the means of two groups, typically used when sample sizes are small.

Dependent Samples

Samples that are related or matched in some way, such as measurements taken before and after a treatment.

Independent Samples

Samples that are selected from two different populations, where the samples are not related.

P-value

The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

Critical Value

The threshold value that the test statistic must exceed in order to reject the null hypothesis.

Sample Mean

The average value of a sample, calculated by summing all observed values and dividing by the number of observations.

Variance

A measure of how much values in a dataset differ from the mean; calculated as the average of the squared differences from the Mean.