Statistical Hypothesis Testing and Confidence Intervals

These flashcards cover key concepts related to hypothesis testing, p-values, confidence intervals, and related statistical terminology.

Null Hypothesis (H0)

A statement that there is no effect or no difference, often denoted as H0: E(X) <= 0.

Alternative Hypothesis (H1)

A statement that indicates the presence of an effect or difference, often denoted as H1: E(X) > 0.

Significance Level (α)

The probability of making a Type I error, typically set at 0.05 or 0.025, indicating how much risk of incorrectly rejecting H0 is acceptable.

Rejection Region

The set of values for which the null hypothesis is rejected in a statistical hypothesis test.

P-value

The probability of obtaining a test statistic at least as extreme as the observed statistic under the null hypothesis.

Confidence Interval (CI)

A range of values derived from sample data that is likely to contain the true population parameter with a certain level of confidence, commonly 95%.

Type I Error

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

Standard Error (SE)

An estimate of the standard deviation of the sampling distribution of a statistic, commonly used in confidence interval calculations.

Central Limit Theorem (CLT)

A statistical theorem stating that, given a sufficiently large sample size, the sampling distribution of the mean will be normally distributed regardless of the original distribution of the population.

Two-tailed Test

A hypothesis test that determines whether a parameter is either greater than or less than a certain value.

One-tailed Test

A hypothesis test that determines whether a parameter is greater than or less than a certain value, but not both.

IID Data

Independent and identically distributed data, which means that data points are independent of one another and come from the same probability distribution.

Symmetric Distribution

A distribution where the left half is a mirror image of the right half, often seen in normal distributions.

Observed Statistic

The calculated value from the sample data that is used to make inferences about the population parameter.

Parameter

A numerical characteristic or feature of a population, such as a mean or standard deviation.

Statistic

A numerical characteristic or feature of a sample, which can be used to estimate a population parameter.