AP Stats Chapter 10 Cheat Sheet (DRAFT) by GSarkar

The standard deviation of the sampling distri­bution of p 1 - p 2 is the square root of the sum of (p 1 )(1-p 1 ) divided by n 1 and (p 2 )(1-p 2 ) divided by n 2 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 [p 1 ] and [p 2 ]

Point Estimate Formula Critical Value Formula (Z*) invNor­m(__%/2 + 0.5) Standard Deviation Formula the square root of the sum of (p 1 )(1-p 1 ) divided by n 1 and (p 2 )(1-p 2 ) divided by n 2 Confidence Interval Formula Point Estimate +/- Critical Value * Standard Deviation

Two Proportion Signif­icance Test

Null Hypothesis p 1 - p 2 = Hypoth­esized Value Altern­ative Hypothesis p 1 - p 2 = Hypoth­esized Value Conditions Random (both), 10% (both), Large Counts (both) Pooled Sample Proportion x 1 + x 2 / n 1 + n 2 (successes / size) Hypoth­esized Value (often 0) Standard Deviation The square root of the sum of (p c )(1-p c ) divided by n 1 and (p c )(1-p c ) divided by n 2 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 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

When the population distri­butions are normal, the sampling distri­bution of x 1 - x 2 is approx­imately normal. Also normal, if both sample sizes are greater than 30 by CLT

If both samples are less than 10% of respective popula­tions, the formula for standard deviation is the square root of the sum of σ1 2 / n 1 and σ2 2 / n 2

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 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 ____.