prob 3

stratified random sampling

multistage cluster random
one stage cluster selected
systematic every n multiplr person

rclick randomly generated number and click 123 on clipboard to freeze. now then you can sort

norm rand var sd 1 mean 0

std norm distribution

norm.s stansardize inverse

xbarplus or minus critical level times sigma divide by (sqrt population size) upper lower bounds confidence intervals

critical level times p times q divide by acceptble level of error 

q is 1 minus p

use 0.5 if unknown to get biggest sample size needed

if p fraction want se is sqrt(p(1-p)/n )

for small samples

1.96sq divide by 4e2 for proportion

for mean (1.96 times var divide by e)sq

e is acceptablenumber of errors

otherwise big samples need fcf finite correction

you dont need a big sample with a big population

sqrt(pop-samp numerator divide by pop-1 denominator) finite correction then multiply standard error

to apply to sample size get samp times pop numerator with samp plus pop minus 1 denominator

pic below for margin of error and fc

1.96 is crit level 

use finite correction if samplesize more than 10 percent of the population

sample mean rej

how large does your sample mean need to be

to reject the null hypothesis, to find the answer you add the

population mean proposed in the

null hypothesis to the product of the

critical z-score at your desired level

of alpha and the population standard error.

When alpha equals .05,

the critical z-score equals 1.645.

zscore formula subtract samp mean from pop mean then divide by standard error

you can tell use crit value from samp mean to rej null

power of test more likely fail reject null hypothesis