Stats and probability

Normally distributed data

Z score (x-mean/sd)

Sample mean- 95% confidence interval

X hat plus or minus 1.96(sd/root n), written - < u < -

Sample mean- hypothesis test

H0: u=- , H1: u does not =-, z= (x hat-u)/(sd/root n), fail to reject or reject

Sample mean- p value

2(1- p(z-score)). If p-value <0.5, reject H0, if p-value >0.5, fail to reject H0

Sample proportions (no mean)- 95% confidence interval

P hat plus or minus 1.96( root ((p hat)(1-p hat)/n)), written -<p<-

Sample proportions- hypothesis test

H0: p= H1: p does not= , p plus minus 1.96root((p hat)(1-p hat)/n)

Expected value

Money x probability