Statistics and Probability Lecture Notes

This set of flashcards covers key terms and concepts from the lecture on statistics and probability, including point estimations, hypothesis testing, and statistical distributions.

Point Estimate

The process of finding a single value from a random sample of the population.

Mean

The average of a set of values, calculated as the sum of the values divided by the number of values.

Variance

A measure of how much values in a data set differ from the mean, calculated as the average of the squared differences from the mean.

Standard Deviation

A statistic that quantifies the amount of variation or dispersion in a set of values.

Confidence Interval

A range of values that is likely to contain the population parameter with a certain level of confidence.

Alpha (α)

The level of significance, representing the probability of making a Type I error.

Null Hypothesis (H₀)

The hypothesis that states there is no significant difference between specified populations.

Alternative Hypothesis (H₁)

The hypothesis that indicates there is a significant difference between populations, which can only be accepted if the null is rejected.

Type I Error

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

Type II Error

The error made when the null hypothesis is not rejected when it is actually false.

Critical Value

The threshold at which the null hypothesis is rejected.

T-Distribution

A probability distribution used for estimating population parameters when the sample size is small and the population variance is unknown.

Z-Score

The number of standard deviations a data point is from the mean.

Test Statistic

A standardized value that is calculated from sample data during a hypothesis test.