Math Medic Ultimate Interpretations Guide - AP Statistics

This set of vocabulary flashcards provides standard interpretations and definitions for one-variable data, two-variable data, probability, sampling distributions, and inference as outlined in the Math Medic guide.

Standard Deviation

The value describing how the context typically varies from the mean.

Percentile

The percentage of values in the context that are less than or equal to a specific value.

z-score

A measurement of how many standard deviations a specific value with context is above or below the mean.

Describe a distribution

A summary that addresses shape, center, variability, and outliers in context.

Correlation ($r$)

A measure of the strength (weak, moderate, or strong) and direction (positive or negative) of the linear association between $x$-context and $y$-context.

Residual

The difference between the actual $y$-context and the predicted value when $x$-context equals a specific number.

y-intercept

The predicted $y$-context when the $x$-context is $0$.

Slope

The amount by which the predicted $y$-context increases or decreases for each additional unit of $x$-context.

Standard Deviation of Residuals ($s$)

The typical distance by which the actual $y$-context is away from the value predicted by the LSRL.

Coefficient of Determination ($r^2$)

The percentage ($r^2 imes 100$) of the variation in $y$-context that can be explained by the linear relationship with $x$-context.

Describe the relationship

A summary of a scatterplot addressing strength, direction, form, and unusual features in context.

Probability $P(A)$

The proportion of times that context $A$ will occur after many, many repetitions of the random process.

Conditional Probability $P(A|B)$

Given context $B$, the probability that context $A$ will occur.

Expected Value (Mean, $\mu$)

The average number of $x$-context expected if the random process of context is repeated for a very large number of times.

Binomial Mean ($\mu_x$)

The average number of success contexts out of $n$ trials after many, many trials.

Binomial Standard Deviation ($\sigma_x$)

The amount by which the number of success contexts out of $n$ typically varies from the mean of $\mu_x$.

Standard Deviation of Sample Proportions ($\sigma_p$)

The amount by which the sample proportion of success context typically varies from the true proportion of $p$.

Standard Deviation of Sample Means ($\sigma$)

The amount by which the sample mean amount of $x$-context typically varies from the true mean of $\mu_x$.

Confidence Interval ($A$, $B$)

An interval that we are a specified percentage confident captures the true parameter context.

Confidence Level

If many, many samples of the same size are taken and a confidence interval is calculated for each, the percentage of intervals that will capture the true parameter in context.

p-value

The probability of getting the observed result or more extreme, purely by chance, assuming the null hypothesis ($H_0$) in context is true.

Conclusion for a Significance Test

The decision to reject or fail to reject $H_0$ and the determination of whether there is convincing evidence for $H_a$ based on comparing the p-value to $\alpha$.

Type I Error

Occurs when the $H_0$ context is true, but we find convincing evidence for the $H_a$ context.

Type II Error

Occurs when the $H_a$ context is true, but we do not find convincing evidence for the $H_a$ context.

Power

The probability that the significance test will correctly reject $H_0$ if the $H_a$ context is true at a specific value.

Standard Error of the Slope ($SE_b$)

The amount the slope of the sample LSRL for $x$-context and $y$-context typically varies from the slope of the population LSRL.