Estimation of Parameters Vocabulary

Key terms and definitions from the lecture on Estimation of Parameters focusing on Point and Interval estimates.

Inferential Statistics

A branch of statistics that pertains to the process of drawing and making decisions concerning a given population based on the data obtained from a sample, focusing on estimation and hypothesis testing.

Estimation

A process of estimating the value of a parameter (or a numerical description of an entire population) from information obtained in a sample.

Estimator

A sample measure used to estimate population measures, such as the sample mean $\bar{X}$ being used to estimate the population mean $\mu$.

Point Estimate of a Parameter

A specific numerical value estimate of a parameter; for example, the sample mean $\bar{X}$ is considered the best point estimate of the population mean $\mu$.

Interval Estimate of a Parameter

Also known as a Confidence Interval, it is an interval or range of values used to estimate a parameter where the parameter is specified as being between two values.

Confidence Level

A degree of confidence representing the probability that the interval estimate will contain the parameter, common levels include 90%, 95%, and 99%.

Alpha Level ($\alpha$)

The probability associated with the area in the tails of the normal curve, where the Confidence Level is calculated as $1 - \alpha$.

Maximum Error of Estimate

The term in the confidence interval formula represented by $z_{\alpha/2} (\frac{\sigma}{\sqrt{n}})$, determining the distance from the sample mean to the boundaries of the interval.

Standard Error of the Population Mean

The standard deviation of the sampling distribution of the sample means, denoted by $\frac{\sigma}{\sqrt{n}}$.

Central Limit Theorem

A theorem stating that as the sample size $n$ gets larger ($n \ge 30$), the shape of the distribution of the sample means approaches a normal distribution regardless of the original population distribution.

Critical Value ($z_{\alpha/2}$) for 90% Confidence

The z-score associated with a 90% confidence level, which is $1.645$.

Critical Value ($z_{\alpha/2}$) for 95% Confidence

The z-score associated with a 95% confidence level, which is $1.960$.

Critical Value ($z_{\alpha/2}$) for 99% Confidence

The z-score associated with a 99% confidence level, which is $2.576$.