Chapter 5: Statistical Inference - Estimation

Flashcards created for reviewing key concepts and vocabulary related to statistical inference and estimation.

Estimation

A method used to infer the value of a population parameter based on sample data.

Point estimate

A single number that serves as the best guess for a population parameter.

Interval estimate

An interval of numbers around a point estimate believed to contain the parameter value; also called a confidence interval.

Confidence interval

An interval estimate that indicates how close the estimate is likely to fall to the parameter value, expressed with a chosen probability.

Margin of error

The amount of error allowed in estimating a population parameter, affecting the width of the confidence interval.

Unbiased estimator

An estimator whose sampling distribution centers around the parameter it estimates.

Biased estimator

An estimator that tends to systematically underestimate or overestimate a parameter.

Efficient estimator

An estimator with a smaller standard error than other estimators, thereby being closer to the parameter.

Sample mean

An average calculated from a sample used as an estimator of the population mean.

Standard error

The standard deviation of the sampling distribution of a statistic, used in calculating confidence intervals.

95% confidence

A level of confidence indicating that if the estimation process were repeated multiple times, 95% of the intervals would contain the true parameter.

Sample proportion

An estimator of the population proportion derived from sample data.

Proportion

A representation that shows the fraction or percentage of a whole.

t-distribution

A probability distribution used when the population standard deviation is unknown, particularly for small sample sizes.

Degrees of freedom (df)

The number of independent values that can vary in an analysis without violating a given constraint.

Z-score

A statistical measurement that describes a value's relationship to the mean of a group of values.

Critical value

A point on the scale of the test statistic beyond which we reject the null hypothesis in a statistical test.

Error probability

The probability that a confidence interval does not contain the true parameter value.

Sample size (n)

The number of observations in a sample that is used to estimate population parameters.

Estimated standard error (se)

An approximation of the standard error that uses sample statistics to estimate population parameters.

Population mean (μ)

The average of a set of values in an entire population.

Sampling distribution

The probability distribution of a statistic based on a random sample.

Null hypothesis

A statement that there is no effect or no difference, often tested in statistical hypothesis testing.

Statistical inference

The process of using data analysis to deduce properties of an underlying probability distribution.

Central Limit Theorem

A theorem stating that the distribution of sample means approaches a normal distribution as the sample size increases.

Random sampling

Selecting a sample from a population in such a way that each member of the population has an equal chance of being chosen.

Point estimator

A statistic that provides a single value estimate of a population parameter.

Confidence level

The probability that the confidence interval contains the true population parameter.

Interval estimation

Estimation technique that provides a range of values within which a parameter is expected to lie.

StatCrunch

A statistical software application that helps in conducting statistical analyses and constructing confidence intervals.

Standard deviation (σ)

A measure of the dispersion or spread of a set of data points.

Point estimate of population proportion (π)

The sample proportion used as an estimator for the population proportion.

Confidence interval for a population mean

An interval estimate for the mean of a population based on a sample mean.

Sample standard deviation

An estimate of the standard deviation of a population based on sample data.

Random sample

A subset of individuals chosen from a larger set, where each individual has an equal chance of selection.

Margin of error formula

The mathematical expression used to determine the range of a confidence interval.

Sampling error

The difference between the population parameter and the sample statistic due to chance.

Sampling distribution of the sample proportion

The distribution of the sample proportion as samples are taken from the population.

Normal distribution

A continuous probability distribution characterized by a bell-shaped curve.

Population standard deviation

The standard deviation of the entire population, often unknown.

Statistical significance

A measure of whether the results of a study are likely to be due to chance.

Sample range

The difference between the maximum and minimum values in a sample.

Estimation methods

Techniques for determining the values of population parameters based on sample statistics.

Survey

A method of data collection that asks participants for information.

Statistical analysis

The process of collecting, organizing, analyzing, interpreting, and presenting data.

Confidence interval for proportions formula

The mathematical expression used to calculate the confidence interval for a population proportion.

Critical value for t-distribution

The t-value that corresponds to a specified level of confidence, found in a t-table.

Confidence interval for mean formula

The arithmetic expression used to create a confidence interval around a sample mean.

Continuous variable

A variable that can take on an infinite number of values within a given range.

Categorical data

Data that can be separated into categories that are distinguished by some non-numeric characteristics.

Sample statistic

A characteristic or measure obtained by using the data values from a sample.

Estimating population parameters

The process of using sample statistics to infer the values of unknown population parameters.

Variable

Any characteristic, number, or quantity that can be measured or counted.

Normal approximation

Assuming that a sufficiently large sample's distribution resembles a normal distribution.

Bell-shaped curve

The graphical representation of a normal distribution.

Statistical model

A mathematical representation of observed data.

Confidence interval interpretation

The explanation of what the confidence interval means in the context of statistical analysis.

Descriptive statistics

Summarizing and describing the characteristics of data.

Inferential statistics

Methods that use sample data to make generalizations about a population.

Percentage estimate

An estimation of a population characteristic expressed as a percentage.

Random variable

A variable whose values depend on outcomes of a random phenomenon.

Continuous probability

The probability of a continuous random variable.