Chapter 7 Vocabulary Flashcards: Confidence Intervals and Estimation

Vocabulary flashcards covering foundational concepts of statistical estimation, confidence intervals, t-distributions, and sample proportions from Chapter 7.

Estimation

The process of estimating the value of a parameter from information obtained from the sample.

Point Estimate

A specific numerical value estimate of a parameter.

Unbiased Estimator

An estimator for which the expected value/mean of the estimate(s) obtained from the sample(s) of a given size is equal to the parameter being estimated, represented as $E(X) = \frac{\text{parameter}}{1}$ or $E(X) = \nu$.

Consistent Estimator

An estimator whose value approaches the value of the parameter being estimated as the sample size increases.

Relatively Efficient Estimator

The estimator that has the smallest variance among all statistics that can be used to estimate a parameter.

Interval Estimate

An interval or a range of values used to estimate a parameter, which may or may not contain the value of the parameter being estimated.

Confidence Level

The probability that an interval estimate will contain the parameter, assuming that a large number of samples are selected and that the estimation process on the same parameter is repeated.

Confidence Interval

A specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate.

Margin of Error

The maximum likely difference between the point estimate of a parameter and the actual value of the parameter, also called the maximum error of the estimate.

Robust Statistical Technique

A statistical procedure where the distribution of the variable can depart somewhat from normality, and valid conclusions can still be obtained.

Student's t Distribution

A family of symmetric, bell-shaped probability distributions centered at zero with variance greater than $1$, based on degrees of freedom, used when the population standard deviation $\nu$ is unknown.

Degrees of Freedom

The number of values that are free to vary after a sample statistic has been computed, given by $df = n - 1$.

Population Proportion ($p$)

The ratio of the number of observations that have a characteristic of interest to the total number of observations in a population.

Sample Proportion ($\hat{p}$)

The ratio of the number of observations that have a characteristic of interest to the total number of observations in a sample.