AP Stats: 1.1 - 1.4

Statistically Significant

Unlikely to occur by random chance

Strength of Evidence

How sure we are it's not chance

Sample

The set of our observational units

Sample Size

Number of observational units (n)

Statistic

Summary of the sample (p-hat)

Parameter

The long-run proportion (π or p)

Test of Significance

Measuring the strength of evidence against the chance model (3-S Strategy)

Null Hypothesis

Random chance explanation

Alternative Hypothesis

Special situation explanation

Null distribution

Distribution of simulated statistics from simulating the null hypothesis

3-S Strategy

Statistic, simulate, strength of evidence

Steps of a statistical investigation

Research question, collect data, explore data, draw inferences, conlusions, look back and ahead

Data

Recorded from observational units

Variables

Recorded characteristics of the observational units

Quantitative Variables

Numerical values

Categorical Variables

Category designations

Distribution

The pattern of the data

Random Process

A process that can be repeated an infinite amount of times with predicted outcomes

Simulation

Artificially re-creating a random process to estimate the probability

Anecdotal Evidence

Personal experience or striking example

Dot Plot

Each dot is a statistic

Standardized statistic

(statistic - mean) / (standard deviation)

P-hat

The summary number of the sample - what you really saw - statistic

π

Your prediction for the whole population - not just your sample

P-value

Evidence against the prediction (π) - how unusual was it? - probability

Too unusual to be random (%)

< 5% (p-value)

Binary Variable

only two outcomes

Distribution

how often it happens

Statistic

summary number

Strength of evidence

against random chance

Two-Sided Test

looking for a difference, bigger or smaller

When do we use the two-sided hypothesis?

When there is no prior assumption of the study

What does the standardized statistic specifically measure?

It measures how many standard deviations it is away from the mean

What EXACTLY is the p-value

proportion of statistics in null distribution as extreme as the statistic.