Methods — Sampling & Confidence Intervals: Fundamentals

19 simple concept cards covering the basic language and symbols. Start here, then study the companion Concepts & Equations set. Based on your Sampling and Confidence Interval Teaching Notes.

What is the difference between a population and a sample?

The population is the whole group you want to learn about. A sample is the smaller group you actually measure.

Why do we use samples?

Measuring everyone may take too much time or money. A sample lets us estimate something about the population, but the estimate has uncertainty.

What is a random sample, and why is it useful?

A sample selected by chance. Random selection helps avoid favouring particular people or results, so the sample is more likely to represent the population.

What does it mean for observations to be independent?

Knowing one result does not change the probabilities for another. The sampling formulas in these notes assume independent observations from the same population.

What is the difference between a parameter and a statistic?

A parameter describes the population, such as μ or p. A statistic is calculated from a sample, such as x̄ or p̂, and is used to estimate the parameter.

What do μ, σ and n mean?

μ is the population mean. σ is the population standard deviation. n is the sample size: the number of observations in one sample.

What is the sample mean x̄?

The average of your sample: x̄ = (sum of sample values)/n. It estimates the population mean μ.

What is the difference between p and p̂?

p is the true proportion in the population. p̂ is the proportion in your sample: p̂ = x/n, where x is the number with the characteristic.

What does standard deviation tell us?

How spread out values are around their mean. A small standard deviation means values cluster closely; a large one means they vary more. Variance is standard deviation squared.

What is a sampling distribution?

The distribution of a statistic over all possible samples of the same size. For example, it shows the different sample averages you could get, and how likely they are.

Why can two random samples give different answers?

They contain different observations, chosen by chance. This natural difference between sample results is called sampling variation.

What is a standard error?

The standard deviation of a sampling distribution. It measures how much a sample estimate typically varies from sample to sample.

What does an unbiased estimator mean?

Its average over many repeated samples equals the true population value. It does not consistently overestimate or underestimate, although any one estimate can be off.

What is a normal distribution?

A symmetric, bell-shaped distribution centred on its mean. Probabilities are areas under its curve; the total area is 1.

What does a z-score tell you?

How many standard deviations a value is above or below its mean: z = (value − mean)/(standard deviation). Positive means above; negative means below.

What is a confidence interval?

A range calculated from a sample to estimate an unknown population value. Its basic form is estimate ± margin of error.

What is the difference between margin of error and interval width?

The margin of error E is the distance from the estimate to either end. The full width w is twice that: w = 2E.

When should you use a mean, and when should you use a proportion?

Use a mean for measured amounts, such as average mass. Use a proportion for the fraction with a characteristic, such as the fraction who own a dog.

How do you use percentages in proportion formulas?

Convert them to decimals: 40% = 0.40. A margin of 3 percentage points is E = 0.03; a total width of 6 percentage points is w = 0.06.