Introducing Data Samples - AP Statistics

It indicates the degree of certainty in an estimate. Higher confidence means we're more sure of our estimate.

It can lead to biased results. Sample doesn't reflect true population characteristics.

A list of elements from which a sample is drawn. Must be complete and accessible for valid sampling.

Selecting samples based on ease of access. Quick but often produces biased, non-representative samples.

To test the feasibility of the main study methods. Small preliminary study to test procedures and identify problems.

An estimator that does not converge to the true parameter. Systematically over- or under-estimates the true parameter.

Wider confidence intervals. More variability creates less precise estimates.

More precision in the estimate. Less uncertainty and more accurate parameter estimation.

A sample is a subset; a census includes the entire population. Census is complete; sample is partial population study.

The entire set of individuals or items of interest in a study. Represents the complete group we want to study or make conclusions about.

A numerical characteristic of a population. Fixed value describing the entire population (e.g., population mean $\mu$).

A numerical characteristic of a sample. Calculated from sample data to estimate population parameters.

Sampling error. Natural variation between sample and population values.

Bias resulting from a non-random sample of a population. Occurs when sample doesn't represent population properly.

$\bar{x} = \frac{\sum{x_i}}{n}$. Sum of all sample values divided by sample size $n$.

To make generalizations about a population based on a sample. Uses sample data to draw conclusions about populations.

Every member of the population has an equal chance of selection. Ensures unbiased selection and representative samples.

Dividing the population into subgroups and sampling each subgroup. Ensures representation from each important subgroup.

Dividing the population into clusters and randomly sampling clusters. Useful when population naturally groups into clusters.

Representative sample. Sample characteristics match population characteristics closely.

The distribution of sample means approximates a normal distribution as the sample size becomes large. Foundation for many statistical inference procedures.

$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$. Uses $n-1$ degrees of freedom for unbiased estimation.

$\sigma = \sqrt{\frac{\sum (X_i - \mu)^2}{N}}$. Uses $N$ in denominator since entire population is known.

The sample size is sufficiently large. Usually $n \geq 30$ for the theorem to apply effectively.

Decreases sampling error. Larger samples provide more accurate population estimates.

Use random sampling methods. Random selection eliminates systematic selection bias.

It helps ensure that the sample is representative of the population. Prevents systematic bias in sample selection.

Greater variability in the data set. Data points are spread far from the mean.

Census. Complete enumeration of entire population.