Unit 5 Formulas and Conditions

p-hat meaning

Sample proportion

Mean of sampling distribution p-hat

Mp-hat = p

Standard deviation of sampling distribution p-hat

Op-hat = sqrt(p(1-p)/n))

Mean of sampling distribution of x-bar

M_x-bar = M

Standard deviation of sampling distribution of x-bar

O_x-bar=O/sqrt(n)

Z score for p-hat

Z=(p-hat - Mp-hat)/Op-hat

Z score for x-bar

Z= (x-bar - Mx-bar)/O_x-bar

10% condition

N>10n, must be used to standard deviation formula

10% condition meaning

when 10% condition is met, then Op-hat and Ox-bar can be validly used and individuals can be treated as independent

Central limit theorem

When the condition is met, the sampling distribution of x-bar is approximately normal, n>= 30

Large counts condition

Sampling distribution of p-hat will be approximately normal when np>=10 and n(1-p) >= 10, Must prove BINS before you can do this (being binomial is a condition)