FinalExamTopics(1) - Tagged

Probability

A measure of the likelihood that an event will occur, ranging between 0 and 1.

Complement Rule

The rule stating that the probability of the complement of an event E is P(E^C) = 1 - P(E).

Addition Rule

The rule that states that for mutually exclusive events A and B, P(A or B) = P(A) + P(B).

Multiplication Rule

The rule stating that for independent events A and B, P(A and B) = P(A) x P(B).

Law of Large Numbers

A theorem which states that as the number of trials increases, the empirical probability of an event approaches its theoretical probability.

Hypothesis Testing

A statistical method to determine whether there is enough evidence in a sample to conclude that a certain condition holds for the entire population.

Null Hypothesis (H0)

The hypothesis stating that there is no effect or no difference; it is the default or starting assumption.

Alternative Hypothesis (H1)

The hypothesis that suggests a potential effect or difference that contradicts the null hypothesis.

P-value

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

Type I Error

The error made when rejecting a true null hypothesis; denoted by alpha (α).

Type II Error

The error made when failing to reject a false null hypothesis; denoted by beta (β).

Central Limit Theorem

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

T-distribution

A probability distribution used for hypothesis testing when the sample size is small and/or the population standard deviation is unknown.

Coefficient of Determination (R²)

A measure that explains how much of the variability in the response variable can be explained by the explanatory variable.

Regression Line Equation

The equation of the form y = a + bx, where a is the y-intercept and b is the slope of the line.

Extrapolation

The act of estimating values outside the range of known data points.

Confidence Interval

A range of values that is likely to contain the value of an unknown parameter, estimated from the sample data.