| Term | Definition |
|---|---|
| population | The entire group of individuals or items from which a sample is drawn and about which conclusions are to be made. |
| sample | A subset of individuals or items selected from a population for the purpose of data collection and analysis. |
| statistic | Numerical summaries or measures calculated from sample data, such as mean, median, or standard deviation. |
| variation | Differences in data that occur by chance due to the random nature of sampling, rather than from systematic causes. |
| Term | Definition |
|---|---|
| area | The region under the normal distribution curve, representing the probability or proportion of values within a specified interval. |
| bell-shaped | The characteristic shape of a normal distribution, with a peak at the center and tails that extend symmetrically on both sides. |
| boundaries | The endpoints of an interval that define where a specified area or probability begins and ends in a normal distribution. |
| continuous random variable | A variable that can take on any value within a specified domain, with every interval having an associated probability. |
| inequalities | Mathematical expressions using symbols such as <, >, ≤, or ≥ to describe the relationship between a variable and the boundaries of an interval. |
| interval | A range of values between two boundaries, used to represent a set of outcomes in a normal distribution. |
| normal curve | The bell-shaped graph of a normal distribution that is symmetric and mound-shaped. |
| normal distribution | A probability distribution that is mound-shaped and symmetric, characterized by a population mean (μ) and population standard deviation (σ). |
| probability | The likelihood or chance that a particular outcome or event will occur, expressed as a value between 0 and 1. |
| probability approximation | Using a known distribution (such as the normal distribution) to estimate probabilities for an unknown or complex distribution. |
| standard normal table | A reference table that provides the cumulative probabilities (areas under the curve) for the standard normal distribution. |
| symmetrical | A property of a distribution where the left and right sides are mirror images of each other around the center. |
| z-score | A standardized score calculated as (xi - μ)/σ that measures how many standard deviations a data value is from the mean. |
| Term | Definition |
|---|---|
| approximately normal | A distribution that closely follows the shape of a normal distribution, allowing for the use of normal probability methods. |
| central limit theorem | A theorem stating that when the sample size is sufficiently large, the sampling distribution of the mean of a random variable will be approximately normally distributed. |
| independence | The condition that observations in a sample are not influenced by each other, typically ensured through random sampling or randomized experiments. |
| null distribution | The probability distribution of the test statistic under the assumption that the null hypothesis is true. |
| random sample | A sample selected from a population in such a way that every member has an equal chance of being chosen, reducing bias and allowing for valid statistical inference. |
| sample size | The number of observations or data points collected in a sample, denoted as n. |
| sampling distribution | The probability distribution of a sample statistic (such as a sample proportion) obtained from repeated sampling of a population. |
| simulation | A method of modeling random events so that simulated outcomes closely match real-world outcomes, used to estimate probabilities. |
| statistic | Numerical summaries or measures calculated from sample data, such as mean, median, or standard deviation. |
| Term | Definition |
|---|---|
| biased | A property of an estimator where the average value of the estimator does not equal the population parameter being estimated. |
| estimator | A statistic used to estimate or approximate the value of a population parameter based on sample data. |
| population parameter | A numerical characteristic of an entire population, such as the mean, proportion, or standard deviation. |
| sample statistic | A numerical value calculated from sample data that is used to estimate the corresponding population parameter. |
| unbiased | A property of an estimator where the average value of the estimator equals the population parameter being estimated. |
| variability | The spread or dispersion of data values in a distribution. |
| Term | Definition |
|---|---|
| approximately normal | A distribution that closely follows the shape of a normal distribution, allowing for the use of normal probability methods. |
| categorical variable | A variable that takes on values that are category names or group labels rather than numerical values. |
| independent samples | Two or more separate groups of data where the values in one group do not influence or depend on the values in another group. |
| mean of the sampling distribution | The expected value of a sample statistic; for sample proportions, μp̂ = p. |
| parameter | A numerical summary that describes a characteristic of an entire population. |
| population proportion | The true proportion or percentage of a characteristic in an entire population, typically denoted as p. |
| probability | The likelihood or chance that a particular outcome or event will occur, expressed as a value between 0 and 1. |
| sample proportion | The proportion of individuals in a sample that have a particular characteristic, denoted as p-hat (p̂). |
| sample size condition | The requirement that np ≥ 10 and n(1-p) ≥ 10 must be satisfied for a sampling distribution of a sample proportion to be approximately normal. |
| sampling distribution | The probability distribution of a sample statistic (such as a sample proportion) obtained from repeated sampling of a population. |
| sampling with replacement | A sampling method in which an item selected from a population can be selected again in subsequent draws. |
| sampling without replacement | A sampling method in which an item selected from a population cannot be selected again in subsequent draws. |
| standard deviation of the sampling distribution | The measure of variability in a sampling distribution; for sample proportions, σp̂ = √(p(1-p)/n). |
| Term | Definition |
|---|---|
| approximately normal | A distribution that closely follows the shape of a normal distribution, allowing for the use of normal probability methods. |
| categorical variable | A variable that takes on values that are category names or group labels rather than numerical values. |
| difference in proportions | The difference between two population proportions, calculated as p₁ - p₂, used to compare the prevalence of a characteristic across two populations. |
| difference in sample proportions | The difference between two sample proportions (p̂₁ - p̂₂) used to compare proportions from two different samples. |
| independent populations | Two populations from which samples are drawn such that the selection from one population does not affect the selection from the other. |
| mean of the sampling distribution | The expected value of a sample statistic; for sample proportions, μp̂ = p. |
| normality conditions | The requirements that must be met for a sampling distribution to be approximately normal, such as n₁p₁ ≥ 10, n₁(1-p₁) ≥ 10, n₂p₂ ≥ 10, and n₂(1-p₂) ≥ 10. |
| parameter | A numerical summary that describes a characteristic of an entire population. |
| population proportion | The true proportion or percentage of a characteristic in an entire population, typically denoted as p. |
| probability | The likelihood or chance that a particular outcome or event will occur, expressed as a value between 0 and 1. |
| sample proportion | The proportion of individuals in a sample that have a particular characteristic, denoted as p-hat (p̂). |
| sample size | The number of observations or data points collected in a sample, denoted as n. |
| sampling distribution | The probability distribution of a sample statistic (such as a sample proportion) obtained from repeated sampling of a population. |
| sampling with replacement | A sampling method in which an item selected from a population can be selected again in subsequent draws. |
| sampling without replacement | A sampling method in which an item selected from a population cannot be selected again in subsequent draws. |
| standard deviation of the sampling distribution | The measure of variability in a sampling distribution; for sample proportions, σp̂ = √(p(1-p)/n). |
| Term | Definition |
|---|---|
| normal distribution | A probability distribution that is mound-shaped and symmetric, characterized by a population mean (μ) and population standard deviation (σ). |
| parameter | A numerical summary that describes a characteristic of an entire population. |
| population | The entire group of individuals or items from which a sample is drawn and about which conclusions are to be made. |
| population distribution | The distribution of all values of a variable across the entire population. |
| population mean | The average of all values in an entire population, denoted as μ. |
| population means | The average values of two distinct populations being compared, denoted as μ₁ and μ₂. |
| population size | The total number of individuals or items in an entire population. |
| probability | The likelihood or chance that a particular outcome or event will occur, expressed as a value between 0 and 1. |
| random sampling with replacement | A sampling method where each selected item is returned to the population before the next selection, allowing the same item to be selected multiple times. |
| random sampling without replacement | A sampling method where each selected item is not returned to the population, so each item can only be selected once. |
| sample mean | The average of all values in a sample, denoted as x̄, used as an estimate of the population mean. |
| sample size | The number of observations or data points collected in a sample, denoted as n. |
| sampling distribution | The probability distribution of a sample statistic (such as a sample proportion) obtained from repeated sampling of a population. |
| standard deviation | A measure of how spread out data values are from the mean, represented by σ in the context of a population. |
| Term | Definition |
|---|---|
| difference in sample means | The result of subtracting one sample mean from another sample mean, calculated as x̄₁ - x̄₂. |
| independent populations | Two populations from which samples are drawn such that the selection from one population does not affect the selection from the other. |
| normal distribution | A probability distribution that is mound-shaped and symmetric, characterized by a population mean (μ) and population standard deviation (σ). |
| parameter | A numerical summary that describes a characteristic of an entire population. |
| population distribution | The distribution of all values of a variable across the entire population. |
| population mean | The average of all values in an entire population, denoted as μ. |
| population means | The average values of two distinct populations being compared, denoted as μ₁ and μ₂. |
| population standard deviation | A measure of the spread or dispersion of all values in a population, denoted by σ, which is a parameter of the normal distribution. |
| probability | The likelihood or chance that a particular outcome or event will occur, expressed as a value between 0 and 1. |
| sample mean | The average of all values in a sample, denoted as x̄, used as an estimate of the population mean. |
| sample size | The number of observations or data points collected in a sample, denoted as n. |
| sampling distribution | The probability distribution of a sample statistic (such as a sample proportion) obtained from repeated sampling of a population. |
| sampling with replacement | A sampling method in which an item selected from a population can be selected again in subsequent draws. |
| sampling without replacement | A sampling method in which an item selected from a population cannot be selected again in subsequent draws. |
| standard error | The standard deviation of a sampling distribution, which measures the variability of a sample statistic across repeated samples. |