GES 500 Engineering Statistics: Confidence Intervals

These flashcards cover key vocabulary related to interval estimation, confidence levels, and confidence intervals as part of engineering statistics.

Interval Estimation

A method used to estimate a range of values within which a population parameter is likely to fall.

Confidence Level

The probability that the confidence interval we create captures the true parameter value.

Confidence Interval

A range of values derived from sample data that is likely to encompass the true population parameter.

Large-Sample Confidence Interval

Confidence intervals constructed from sample sizes large enough for the Central Limit Theorem to apply.

Central Limit Theorem

A statistical theory that states that the distribution of the sample mean approaches a normal distribution as the sample size increases.

Normal Distribution

A symmetric probability distribution characterized by its bell-shaped curve, defined by two parameters: mean and standard deviation.

Cumulative Distribution Function (CDF)

A function that describes the probability that a random variable takes on a value less than or equal to a certain value.

Parameter 

A measurable characteristic of a population, such as the mean or standard deviation.

Point Estimator

A statistic used to estimate the value of an unknown parameter.

Non-unique Solution

A situation where a statistical equation can have multiple valid solutions.

Symmetry Rule

A principle used to determine bounds in confidence intervals for symmetric distributions.

Standard Normal Variable (Z)

A normal random variable with a mean of 0 and a standard deviation of 1.

Estimation Error

The difference between the estimated value and the actual value of the parameter.

Probabilistic Distribution

A function that describes the likelihood of obtaining the possible values of a random variable.

Unbiased Estimator

An estimator whose expected value is equal to the true parameter value.

Student's t-Distribution

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

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis.

Concentration of Data

The extent to which data points are clustered around a central point, typically the mean.

Bernoulli Trial

A random experiment where there are only two possible outcomes, typically referred to as 'success' and 'failure'.

Halfwidth of Confidence Interval

The distance from the center of the confidence interval to either of its endpoints.

Estimation of Confidence Intervals

The process of calculating the range of values that is likely to include an unknown parameter based on sample data.