Acorn Book (and where they are in IPS) ( (I) Descriptive ...
Transcript of Acorn Book (and where they are in IPS) ( (I) Descriptive ...
n(The sample mean of a data set.)
AP Statistics: Formulas from the Acorn Book and what they mean(and where they are in IPS)
( (I) Descriptive Statistics
Ix;• X=
• sx = IlL (x , - x) 2 (The sample standard deviation.s1n -1
• s =p
(nl-1)s~ + (n2-1)s~(Pooled estimator oj G, the population
(nj-1) + (n2-1)standard deviation for two-sample tprocedures. Assumes populations haveequal variances. ., Generalized inANOVA.)
• y = bo + bjx (The least squares regression line in which bo estimatesf30 and b J estimates f3 J 1 .
•L (Xi - x)(y; - y)
L (X; - X)2(The slope of the least squares regression
• b =y--bxo J
line.) _
(The y-intercept of the least squares regression line.) .~.~,
• (The correlation coefficients:
• b J = r:r. (Linear relationship between the slope of the regression linesx
and the correlation coefficient.)
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Source: Duane Hinders\ r:: \
! .
•
L (Yi - y)2n - 2
Sb =, JUx, - i)'
(II) Probability
(Standard error of the slope of the regression
line.)
• peA u B) = prAY + PCB) - peA n B) (Addition Rule for Unions ofTwo Events) .. ..
• peA I B) = peA n B) (Conditional probability of A given B.)PCB)
• (Mean (expected value) of a discrete random
variable X.). -
• (Variance of a discrete random
variable X.):If X has a binomial distribution with parameters nand p , then:
• P(X = k) = (;) pk(J ~ »:: (Probability of getting exactly k successes
in n observations of an event that occurswith probability, ) ~. ,
• J..ix = np (Mean of a binomially distributed random variable.) .;
(Standard deviation of a binomially distributedrandom variable. )~_ -
(Mean of a sampleproportion.) ..
• a =A~np(l - p) .
•
• (Standard deviation of a sample proportion.) ..
2Source: Duane Hinders
i ~ C.
('\ ...•......
If X has a normal distribution with mean J.l and standard deviation a, then:
(Mean of a sampling distribution of sample means.) _, '•l, '
•a
a--x - rn (Standard deviation of a sampling distribution of sample means
-- standard error of the mean. }
(III) Inferential Statistics
Single Sam pie
mean a d.f. = n-l)(x) in
proportion ~p(1 n-P) :-!
(p)
········s· ···························S.. '.r~.·d··n t·· .......... ~.~I~tl~ ~Q~{ ~y.~~'QQ .
T S I
<wo amrne
Statistic Standard Deviation
difference of means ~ 0;(unequal variances) ~ n1 + nz
- ".=-;, ,(x 1- x z) .'
.. ' ,
(d.f. = min{nJ-I,n2-1})
difference of means.
a~ 1 + 1/
(equal variances) (x]- x) (d.f. = n] + n2 -2)n 1 nz
difference of proportions (jJ - Pz) Pj(1 - p) Pz(1 - pz) ,(unequal variances) .1\ +
n1 nz
difference of proportions J0T(equal variances) (PI -pz) ~p(1 - p) - + - ,0'
n 1 nz
. .. (observed - expectedt'Chi-square test statisnc = L~------!------::-expected
, (For a two-way table, d.f. = (r - l)(c - 1); for Goodness-of-Fit. d.f = n - 1)
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Source: Duane HindersIC:-,