PANIC for two proportions
P: is the same as normal except u declare two "true proportions of blah" (p1 and p2)
A: is the same as normal, say both populations are independent (10% of population blah blah), assume simple random sample, assume normality - for normality you do np > 10 and n(1-p) > 10 except now you have p1 and p2 so you do 4 tests for normality total
N: is name the test so you can just say the formula which is: Confidence interval = (p1-p2) +/- z*sqrt( (p1(1-p1)/n1 + (p2(1-p2))/n2 )
I: use the formula which gives you two numbers cuz +/- and that's ur confidence interval...if your confidence interval has 0 in it like example (-0.1, 5) it's kinda like saying your interval includes the possibility of p1-p2=0 or p1=p2 which is what null hypothesis is in the phantoms problem... so if you have 0 in your confidence interval then you "fail to reject null hypothesis" AKA if the problem is asking to change something you say no...so if you don't have 0 in the confidence interval it's like rejecting null and you say yes to whatever change (this is like the "context" part so like you'll know what to do when u see the word problem) Also to check your answer u can use 2PropZInt test on calculator
C: state ur conclusion (same way as panic normally: "we are 95% confident blah blah context stuff"
PHANTOMS for two proportions
P: same as PANIC
H: same as regular phantoms like exactly the same except it's gonna be comparing p1 to p2 instead of p to some proportion
A: same as PANIC
N: name test so formula is z = (p1-p2)/sqrt(pc(1-pc)/n1 + pc(1-pc)/n2)
T: do the test. you can find pc by doing (x1+x2)/(n1+n2) so get pc and plug it into formula and get z.
O: use 2PropZTest on calculator and get your p value.
M: Your significance level alpha...use that and compare to ur p value and if p < a, reject null, if p >= a, fail to reject. if they don't give you alpha then u assume alpha is 0.05
S: conclusion (there is sufficient/insufficient evidence blah blah context)