Statistics Project for MRMATHEXPERT ONLYYYYYYYY

S 2 2

t = - where s x-l -x -2 iL + - and S l _ i2 fl 1 11 2

S 1

n

2\2

—+— I n )

df= 2 1L

(fl2

n 1 ) n 2 j +

n 1 —i 112 1

integer

always rounded down to the neare St

Case III: Two independent samples, a & a 2 unknown and unequal AND both groups normally distributed or both samples> 30

Hypothesis Test (under assumption that ii1=2): (2-SampTTest)

Confidence Interval: (2-SampTlnt)

( tdf where df is defined as above

Case IV: Two dependent (paired) samples, either normally distributed or n >30

For each pair, calculate the difference dx 1 -x2 . The calculate the simple mean and standard deviation of these differences, J and 5d•

Hypothesis Test (under assumption that true mean difference = 0): (Ttest)

d Sd t=— wheres= —

S

Confidence Interval: (Tinterval)

± tn_I S

Case V: Two large and independent samples for binomial proportions

Hypothesis Test (under the assumption p 1 =p2):(2-PropZTest)

z = where sP' PZ = p(1 — p)(] + 1 ) and p = x, + x2 — n, p, + n 2 p2

s n , nz n, + n2 n, + n2 P1 - P2

Confidence Interval: (2-PropZlnt)

(p, - p 2 )±zs where this time s A-Pz — ,I p ^ (I + —p,) p 2(1—pz)

V

Case VI: Two independent sample that aren't normal and both samples sizes are < 30

Drop back 15 and punt.