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Standardized Values

Values for which the units have been systematically eliminated, allowing for comparison, even if the original variables had different scales and/or units

z-Score

Standardized value that identifies how many standard deviations a value is from the mean; z-scores don't change a distribution's shape, but force the mean to 0 and the standard deviation to 1

Normal Model

Appropriate for distributions that are roughly "bell-shaped" amd unimodal symmetric; represented by the notation N(mean, SD)

Nearly Normal Condition

The shape of a distribution must be roughly "bell-shaped" and unimodal symmetric in order to use the Normal Model

Normal Probability Plot

Display used tp assess whether or not a distribution is approximately Normal... if the plot is relatively straight, then the data satisfies the Nearly Normal Condition

68-95-99.7 rule -> "Empirical Rule"

For a Normal Model, about 68% of the data values fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations

Standard Normal Model

The Normal Model with mean 0 and standard deviation 1; N(0, 1)

Normal Percentile/P-value

Gives the percentage of values in a Standard Normal distribution found at or below a given z-score. Also known as the P-value, since it is the probability that you will land at that z-score or below in a Standard Normal distribution

Random Variable

Denoted by a capital letter such as X, assumes any of several different values as a result of a random event

Discrete Random Variable

Random variable that can only take on distinct numerical values within a range of values

Continuous Random Variable

Random Variable that can take on any numerical value within a range of values

Probability Model

Function that associates a probability with each value of a discrete random variable, denotes P(X=xi), or with any interval of values of a continuous random variable, e.g. P(X ≤ xi)

Expected Value

The theoretical long-run mean value of a random variable (the center of its model)

Deviation

The difference between a particular value in a probability model and the expected value (actual - expected = xi - ux)

Variance

The expected value of the squared deviation from the mean; the square of the standard deviation

Standard Deviation

The square root of the variance; the average distance of a random variable's value from its expected value (center)

Bernoulli Trials

Trials that meet the following conditions:
- Binary -> only two possible outcomes, success or failure
- Independence
- Succes probability (p) is constant... thus so is the failure probability (q)

Geometric Probability Model [BITS]

Denotes Geom(p), determines the probability of the first success occuring on trial x for Bernoulli trials

10% Condition Independence

Trials can be considered sufficiently independent if the sample size is less than 10% of the population from which it will be drawn

Combination

The number of ways to have k successes in n trials, called "n choose k"

Binomial Probability Model [BINS]

Denoted binom(n,p), determines the probability of x successes in n Bernoulli trials

Success/Failure Condition

A Binomial Probability Model has a sufficient sample size to be considered nearly Normal if at least 10 successes and 10 failures are expected, thus np ≥ 10 and nq ≥ 10

Sampling Distribution Model

The distribution that shows the behavior of a statistic (value from a sample) with its sampling variability over all possible samples of the same sample size n

Central Limit Theorem

The sampling distribution model of means/proportions is approximately Normal for "large enough" sample size n, as long as the observations are independent

Law of Diminishing Returns

The standard deviation of a sampling distribution model decreases by the square root of the sample size... e.g. quadruple the sample size -> standard deviation cut in half

Large Enough Sample Condition

A "large enough" sample size is necessary to ensure the CLT "kicks in" (Success/Failure Condition for proportions; n ≥ 30 often sufficient for means if data is not severely skewed)