Inference Formula Sheet – AP Statistics

Test

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Assumptions

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Null Hypothesis

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Test Statistic

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Confidence Interval

One –sample z-test
for inference of
population means / Normal population, random sample, and
s known / Ho: m = m0 / z = /
Two –sample
z –test for inference
on population means / Two independent normal populations, random samples and
s1 and s2 known / Ho: m1 = m2
or
Ho: m1 - m2 = 0 / /
One-sample t-test for population means / Normal population (n>30 or check sample),
random sample.
(s unknown) / Ho: m = m0 / t = ; df = n – 1 / ; df = n – 1
Two-sample t-test for inference on population means / Two independent normal populations (n>30 or check samples),
random sample.
(s1 and s2 unknown) / Ho: m1 = m2
or
Ho: m1 - m2 = = 0 / t = ;
df =the minimum of n1 – 1 or
n2 – 1 or the exact value from a computer or calculator. /
Paired t-test:
One sample t-test on the differences of dependent sample means / Normal distribution of the population of differences of 2 dependent means,
random sample.
(s unknown) / Ho: md = 0 / t = ; df = n – 1 / ; df = n – 1
One –Proportion
z-test / Random sample, population 10 times sample size
np 10 and n(1-p) 10 / Ho: p = po / z = /
Two –Proportion
z- test / Random sample, populations are 10 times sample sizes
n1p1 10, n1(1-p2 ) 10
n2p2 10, n2(1-p2) 10 / Ho: p1 = p2
or
Ho: p1 - p2 = 0 / /
Linear Regression
inference on the slope of a line / Residuals are normally distributed and have the same s everywhere along the line. / Ho: b = 0 / t = ; df = n – 2 / slope ± t* S.E.slope
Chi Square Goodness of Fig / Random sample and all expected counts 5 / Ho: Observed distribution is same as expected /
Chi Square test for
homogeneity of proportions / Random samples and all
expected counts 5 / Ho: Data is same for all populations /
Chi Square test for
independence / Random sample and all
expected counts 5 / Ho: No association between variables or the variables are independent from each other. /