STATISTICS 11: Estimating Parameters

DEF OF TERMS BASED ON THE BOOK. In-depth notes for this semester: https://docs.google.com/document/d/1fF2-I6oefjX7Jl7cw4vudFEyFENuN1muDb3NfDPnYwI/edit?usp=sharing

Statistical Inference

Making conclusions or generalization about the population based on the study of samples.

Estimation

This can be either a point estimate or an interval estimate—the process of assigning a value or values to a population parameter based on a sample statistic.

Point Estimate

It is a single value that estimates the population parameter, such as x̄ as estimate for μ, or s as estimate for σ.

Interval Estimate

It is sometimes called confidence interval and is a range or interval (with lower and upper limits) used to estimate the population parameter. It is usually in the form a < θ < b, which tells that the estimated parameter (Θ) is between two values (a and b) at a certain level of confidence.

Confidence Interval

 It is an interval estimate with an associated confidence that it contains the unknown parameter.

Confidence Level

It is a part of all possible samples (in percent) taken from the same population that can be expected to include the true population parameter.

• For example, a 95% confidence level means 95% of the intervals contain the true population parameter.

Inferential Statistics

It is composed of estimating the population parameter and hypothesis testing.

Descriptive Statistics

It is a method for summarizing and organizing information

Estimate

A value assigned to a population parameter based on a sample.

Central Limit Theorem

A theorem stating that for large samples (n ≥ 30), the sampling distribution of the sample mean becomes approximately normally distributed with mean μ and standard deviation σ/√n.

Confidence Coefficient

This is denoted by 1 – α. It is the probability that an interval contains the population parameter.

Limits

The endpoints of the interval.

Margin of Error

It is the maximum likely difference (in percent) between sample mean and the real population value μ.