Statistics Formula Sheet1. Confidence interval for m:a) / 2 / 2,x z x zn na as s� �- +� �� � if sis known. / 2za is from the Z chart.b) / 2, 1 / 2, 1,n ns sx t x tn na a- -� �- +� �� � if sis unknown. / 2ta is from the 1nt-. (Use a / 2zif n > 30)2. Confidence interval for s: The denominator comes from 21nc- chart.2 22 2/ 2, 1 1 / 2, 1( 1) ( 1),n nn s n sa ac c- - -� �- -� �� �� �3. Confidence interval for a population proportion:/ 2 / 2ˆ ˆ ˆ ˆ(1 ) (1 )ˆ ˆ,p p p pp z p zn na a� �- -- +� �� �� �4. Hypothesis Testing:Be sure to include:Ho and Ha (Always put equality in Ho)The value of the data test statistic (z, t, or whatever)A properly labeled picture for any non-computer problemThe p-value for any computer problemReject or Fail to RejectThe conclusion in words0/xznms-=0/xts nm-=2220( 1)n sc-=s0 00(1 )ˆp pnp pz--=Determining the probability of Type II Error if the true mean is Tm and not 0m1. Testing 00::HoHam mm m=> 2. Testing 00::HoHam mm m=<0(Type II Error) ( )/TP P Z znam ms-= < - 0(Type II Error) ( )/TP P z Znam ms-= - +