Statistics Inference and Probability Concepts

These flashcards cover key vocabulary and definitions related to statistical inference and probability concepts.

One-sample t-interval for μ

A statistical method used to estimate the population mean when the population standard deviation is unknown.

One-sample z-test for p

A hypothesis test used to determine if the proportion from a single sample is significantly different from a hypothesized population proportion.

Two-sample t-test for μ1– μ2

A test comparing the means from two different populations to see if they are significantly different.

Chi-Square Test for Homogeneity/Independence

A statistical test used to examine the relationships between categorical variables.

P-value

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

Type I error

The error that occurs when the null hypothesis is true but is rejected.

Type II error

The error that occurs when the alternative hypothesis is true but the null hypothesis is not rejected.

Confidence interval

A range of values derived from a data set that is likely to contain the value of an unknown population parameter.

Sampling distribution

The probability distribution of a statistic obtained by selecting random samples from a population.

Central Limit Theorem

A theorem stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

Unbiased estimator

An estimator whose expected value equals the parameter it estimates.

Random sampling

Selecting a subset of individuals from a statistical population in such a way that every individual has an equal chance of being chosen.

Blocking in experiments

A technique used in experimental design to reduce the variability of a response variable by grouping similar experimental units together.

Discrete variable

A variable that can take on a countable number of values.

Continuous variable

A variable that can take on an infinite number of values within a given range.

Mean of a binomial distribution

The average number of successes in a binomial experiment, calculated as μ = n * p.

Standard deviation of a binomial distribution

A measure of the spread of a binomial distribution, calculated as σ = √(n * p * (1 - p)).

Law of Large Numbers

A principle that describes the result of performing the same experiment a large number of times.

Mutually exclusive events

Events that cannot occur at the same time.

Conditional probability

The probability of one event occurring given that another event has already occurred.

Z-score

A statistical measurement that describes a value's relationship to the mean of a group of values.