gilbreath ap stats semester one review

10% Condition

Ensure sample size is small enough to assume independent trials.

Success/Failure Condition

A condition that determines the sufficiency of sample size for estimating proportions.

Central Limit Theorem

States that the sampling distribution of the sample means will be approximately normally distributed if the sample size is sufficiently large (n ≥ 30).

Simple Random Sample

A sampling method where every individual has an equal chance of being selected.

Experiments vs. Observational Studies

Experiments involve treatment to imply cause and effect, while observational studies do not.

Graphical Representations

Methods used to visualize data, such as histograms or box plots.

Mean vs. Median in Skewed Distributions

In skewed distributions, the mean is pulled in the direction of the skew, while the median is more stable.

Outliers

Data points that differ significantly from other observations, calculable by z-score or five-number summary.

Interpreting Slopes of Regression Lines

The slope indicates the change in the response variable for a one-unit increase in the explanatory variable.

R-squared

A statistical measure that represents the proportion of variance for a dependent variable that's explained by an independent variable.

Probability

The measure of the likelihood that an event will occur.

Binomial Distributions

Probabilities of a fixed number of successes in a fixed number of independent trials.

Conditional Probabilities

The probability of an event occurring given that another event has already occurred.

Addition Rule of Probabilities

The rule stating that the probability of the occurrence of at least one of two events is equal to the sum of their probabilities minus the probability of their intersection.

Multiplication Rule of Probabilities

States that the probability of two independent events occurring together is the product of their individual probabilities.

Stem-and-Leaf Plot

A graphical representation used to display quantitative data while retaining original data values.

Shape and Center of Distribution

Includes understanding median, range, and any unusual features identified in the data.

Hypothesis Testing Steps

Formulate hypotheses, determine significance levels, calculate test statistics, and make decisions based on p-values.

Power of a Test

The probability that the test correctly rejects a false null hypothesis.

Categorical vs. Quantitative Data

Categorical data represents characteristics; quantitative data represents numerical values.

Chi-Square Tests

Used to determine if there's a significant association between categorical variables.

Data Transformations

Applying mathematical operations to data to meet statistical assumptions, such as normalization.

Mean

The average of a set of values, calculated by summing all values and dividing by their count.

Median

The middle value in a data set when arranged in ascending order.

Mode

The value that appears most frequently in a data set.

Probability of Drawing a Card

Calculating the likelihood of drawing a specific card from a standard deck, expressed as a fraction and a percentage.

95% Confidence Interval

An interval estimate that is believed to contain the true population parameter with 95% certainty.

Chi-Square Test for Independence

Used to determine if there is a significant association between two categorical variables in a contingency table.

p-value

The probability of obtaining a test statistic as extreme as, or more extreme than, the value observed, under the assumption the null hypothesis is true.

Confidence Interval (CI)

CI = sample statistic ± (critical value)(standard error).

z-score

z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Standard Error (SE)

SE = σ/√n, where σ is the population standard deviation and n is the sample size.

Effect Size

A measure of the size of a difference or the strength of a relationship, useful for determining the practical significance of results.

Understanding Distributions

Assessing the shape and characteristics such as center, spread, and outliers.

Practice Problems Review

Revisiting problems tackled in class to reinforce learning and application of concepts.

Exam Preparation Strategy

Emphasizing comprehension over memorization while familiarizing with key terms and concepts.

Understanding Treatment in Experiments

Experiments require treatment application to establish causal relationships.

Interpreting Results

Analyzing outcomes in relation to statistical measures and significance.

Statistical Models Probabilities

Calculating z-scores and probabilities based on applied statistical models.

Box Plot Interpretation

A graphical summary of data that shows the median, quartiles, and potential outliers.

Z-score Method

A method to identify outliers by measuring how many standard deviations a data point is from the mean.

Five-Number Summary

A summary that includes the minimum, first quartile, median, third quartile, and maximum of a dataset.

Visual Data Analysis

Utilizing graphical methods to analyze and interpret data distributions.

Normal Distribution Characteristics

A symmetric, bell-shaped distribution defined by its mean and standard deviation.

Sample Size Effect on Power

Increasing sample size generally increases the power of a statistical test.

Significance Levels in Testing

A threshold set to determine when to reject the null hypothesis in hypothesis testing.

Estimating Sample Statistics

Calculating estimates based on data from a sample.

Critical Value

A point that separates the region where the null hypothesis is rejected from where it is not.

Transformation Impact on Data

Changes the scale or distribution of data to meet statistical assumptions.

Sampling Distribution Characteristics

Describes how the sample mean is distributed across all possible samples from the population.