Show Menu
Cheatography
  1. Home >
  2. Cheat Sheets >

AP Stats Chapter 10 Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Two Proportion Confidence Interval

Shape
When the large counts rule is met, the sampling distri­bution of p1 - p2 is approx­imately normal
Center
The mean of the sampling distri­bution is p1 - p2
Spread
The standard deviation of the sampling distri­bution of p1 - p2 is the square root of the sum of (p1)(1-p1) divided by n1 and (p2)(1-p2) divided by n2 as long as each sample is no more than 10% of its popula­tion.
Conditions
Random (both samples must be random), 10% (both samples less than 10% of respective popula­tion), Large Counts (for both samples indivi­dually)
Calculator
2-Prop­ZIn­terval
Interp­ret­ation
We are __% confident that the interval from __ to __ captures the true difference of [p1] and [p2]
Point Estimate Formula
p1 - p2
Critical Value Formula (Z*)
invNor­m(__%/2 + 0.5)
Standard Deviation Formula
the square root of the sum of (p1)(1-p1) divided by n1 and (p2)(1-p2) divided by n2
Confidence Interval Formula
Point Estimate +/- Critical Value * Standard Deviation

Two Proportion Signif­icance Test

Null Hypothesis
p1 - p2 = Hypoth­esized Value
Altern­ative Hypothesis
p1 - p2 = Hypoth­esized Value
Conditions
Random (both), 10% (both), Large Counts (both)
Pooled Sample Proportion
x1 + x2 / n1 + n2 (successes / size)
Statistic
p1 - p2
Parameter
Hypoth­esized Value (often 0)
Standard Deviation
The square root of the sum of (pc)(1-pc) divided by n1 and (pc)(1-pc) divided by n2
Test Statistic Formula
Statistic - Parameter / Standard Deviation
Calculator
2PropZTest
Areas of Error
Not a random sample = can't generalize results, cause and effect vs correl­ation
IMPORTANT
If experi­mental units are randomly selected, check the 10%, otherwise techni­cally not necessary
Ideal for Conclu­sions about Popula­tions
Data from Two Indepe­ndent Random Samples
 

Two Mean Confidence Interval

Shape
When the population distri­butions are normal, the sampling distri­bution of x1 - x2 is approx­imately normal. Also normal, if both sample sizes are greater than 30 by CLT
Center
μ1 - μ2
Spread
If both samples are less than 10% of respective popula­tions, the formula for standard deviation is the square root of the sum of σ12 / n1 and σ22 / n2
Conditions
Random (both samples are indepe­ndent and random or from two groups in a randomized experi­ment), 10% (both), and Normal­/Large (popul­ation distri­butions are normal or sample size greater than 30)
Calculator
2SampTInt
Interp­ret­ation of a Confidence Level
If we take many samples of size _ of _ and of _ of _ and find the __% confidence interval for each sample, __% of the confidence intervals will capture the difference in the mean number of ____.
Interp­ret­ation of Confidence Interval
We are __% confident that the interval from __ to __ captures the true difference in the __
State
We want to estimate μ1 - μ2 at the __% confidence level where μ1 is __ and μ2 is __
Point Estimate Formula
x1 - x2
Critical Value Formula (t*)
invT(p/2 + 0.5, smaller n df)
Standard Deviat­ion­/Error Formula
The square root of the sum of σ12 / n1 and σ22 / n2
Confidence Interval Formula
Point Estimate +/- Critical Value * Standard Deviation

Two Mean Signif­icance Test

Null Hypothesis
μ1 - μ2 = Hypoth­esized Value
Altern­ative Hypothesis
μ1 - μ2 = Hypoth­esized Value
Conditions
Random (both), 10% (both), Normal­/Large (both)(no strong skew, outliers, or greater than 30)
Statistic
x1 - x2
Parameter
μ1 - μ2
Standard Deviation
The square root of the sum of s12 / n1 and s22 / n2
Test Statistic Formula (T)
Statistic - Parameter / Standard Deviation
Calculator
2SampTTest
Interp­ret­ation of p-value
Assuming the null hypothesis is true, there is a __ probab­ility of getting a difference in ___ just by the chance involved in random assign­men­t/v­ari­ability

Paired Data vs Two Samples

Paired Data
Two Samples
Subjects were paired and the split at random into the two treatment groups or each subject received both treatments in a random order
Experi­mental groups were formed using randomized design or two indepe­ndent random samples were taken from the population