QMB Stats 7 + 8 Notes

population

representation of all possible subjects of interest

sample

a subset of a population

nonprobability sampling

a sample in which the probability of a population member being selected for the sample is not known

convenience

sampling used when sample values are selected simply because they are easily accessible

probability sample

A is a sample in which each member of the population has a known, nonzero, chance of being selected for the sample

simple random

Example of probability sampling where a sample in which every member of the population has an equal chance of being chosen

systematic

Example of probability sampling where every Xth member of the population is chosen for sample size, the value of X is determined by dividing the size of the population (N) by the size of the sample (n)

resampling

a statistical technique where many samples are repeatedly drawn from a population

parameter

values that describe some characteristic of a population, such as its mean or median

statistic

values calculated from a sample, such as the sample’s mean or median

sampling error

defined as the difference between the sample statistic and the population parameter

nonsampling errors occur as a result of

- ambiguous survey questions
- questions that lead respondents to a certain “correct” answer
- data collection errors

Central Limit Theorem

sample means from samples of sufficient size, drawn from any population, will be normally distributed

The Effect of the Sample Size on the Sampling Distribution

As the sample size increases, the standard error of the mean becomes smaller, which in turn reduces the sampling error

census

process of recording information from the entire population of interest

sampling distribution of the proportion

describes the pattern that sample proportions tend to follow when randomly drawn from a population

Formula for the Systemic Sampling Constant

Formula for the Sampling error of the Sample Mean

For any population

the average value of all possible sample means computed from all possible random samples of a given size from the population is equal to the population mean

the standard error of the mean

Formula for the Z score for the Sample Mean

Using the Central Limit Theorem to Test Claims

Formula for the Standard Error of the Mean (Finite Population)

Finite Population Correction Factor

Formula for Sample Proportion

Formula for the Standard Error of the Proportion

Formula for the z-score for the Sample Proportion

Formula for the Standard Error of the Proportion (Finite Population)

point estimate

a single value that best describes the population of interest

interval estimate

provides additional information about variability

confidence interval for the mean

an interval estimate around a sample mean that provides us with a range within which the true population mean is expected to lie

confidence level

defined as the probability that the interval estimate will include the population parameter of interest

The formula for the Confidence Interval for the Mean (σ Known)

critical z score

significance level (α)

represents the probability that any given confidence interval will not contain the true population mean

The Margin of Error (MEx)

the width of the confidence interval between a sample mean and its upper limit or between a sample mean and its lower limit

Formula for the Sample Standard Deviation

t-distribution

a continuous probability distribution featuring a bell-shaped curve, symmetry around the mean, and can be changed using degrees of freedom

Formulas for the Confidence Interval for the Mean (σ Unknown)

Calculating Confidence Intervals for Proportions

confidence interval for the proportion

interval estimate around a sample proportion that provides us with a range of where the true population proportion lies