critical value standard error of statistic ± Chi-square statistic: ( ) 2 observed expected expected χ − = ∑ 2 AP Statistics 2020 Formulas and Tables Sheet
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P(at least 1 failure) = 1 pn 5 ) Binomial Distribution Formula for x=exact value 6 ) Mean (Expectation) (x) p μ = E = n 7 ) Variance and Standard Dev pq σ2 = n
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same formula after adding 2 successes and two failures to the data • z test statistic for H0 : p = p0 (large SRS): z = ˆp − p0 √p0(1 − p0) n P-values from N( 0,1)
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critical value standard error of statistic ± Chi-square statistic: ( ) 2 observed expected expected χ − = ∑ 2 AP Statistics 2020 Formulas and Tables Sheet
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I.Descriptive Statistics
1 ii xxxnn 221 11 ixi xxs xxnn
ˆy abx y abx
1 1 ii xy xxyyrn ss y x brs sII.Probability and Distributions
PA BPA PB PAB
|PA BPABPB Probability Distribution Mean Standard Deviation Discrete random variable, X X EX xP i x i X x iX Px i 2If ܺ
with parameters n and p, then: n PXxp x 1p nx ©x where x0,1,2,3 ,,n X np X np1pIf ܺgeometric distribution
with parameter p, then: PXx1p x1 p where x1, 2,3, 1 X p 1p X pIII.Sampling Distributions and Inferential StatisticsStandardized test statistic:
statisticparameter standard error of the statistic Confidence interval: statisticcritical va luestandard error of statisticChi-square statistic:
2 observedexpect ed expected 2*S tandard deviation is a measurement of variability from the theoretical population. Standard error is the estimate of the standard deviation. If the
standard deviation of the statistic is assumed to be known, then the standard deviation should be used instead of the standar
d error. III.Sampling Distributions and Inferential Statistics (continued)Sampling distributions for proportions:
Random
Variable Parameters of
Sampling Distribution Standard Error
of Sample StatisticFor one
population: pˆ 1p pˆ n pˆ p ppˆ1 s pˆ n pˆFor two
populations: p 1 pˆˆ 2 p ppˆˆ1 12 p p 1 1 pp 12 ppˆˆ 12n 1 p1 2 2 n 2 pˆs 11ppˆˆ
12 ppˆˆ 12n 1 1 pˆ 2 n 2When p
1 is assumed: p 2 spp1ˆˆ1
ppˆˆc c 12 nn1 1 2XXpˆ
1 c nn where 2 12Sampling distributions for means:
Random
Variable
Parameters of Sampling Distribution
Standard Error
of Sample StatisticFor one
population: X X X n ss X nFor two
populations: XX 12 XX1 12 2 2212 XX 12 n 12 n ss 2 s 1 XX 12 nn 1 2 2 2