STAT1008 Lecture Notes - Lecture 27: Statistic, Null Hypothesis, Confidence Interval
STAT1008 Week 9 Lecture C
● One proportion or two?
○ Two proportions: there are two separate categorical variables
○ One proportion: there is only one categorical variable
○ E.g. Windows vs Mac
■ You want to compare the proportion of students who use a Windows-
based PC to the proportion who use a Mac
■ This is:
● Inference for one proportion since there is only one categorical
variable (type of computer used)
○ E.g. Studying abroad
■ You want to compare the proportion of students who study abroad
between those attending public universities and those at private
universities
■ This is:
● Inference of two proportions since you have two categorical
variables (students abroad and attending public or private
universities)
○ E.g. Instate vs outside
■ You want to compare the proportion of in-state students at a university to
the proportion from outside the state
■ This is:
● Inference of one proportion since you have one categorical
variable (in or out of state)
○ E.g. Financial aid
■ You want to compare the proportion of in-state students who get financial
aid to the proportion of out-of-state students who get financial aid
■ This is:
● Inference of two proportions since you have two categorical
variables (instate or out of state and financial aid)
● SE for P hat1 - P hat2
○ The standard error for phat1 - phat2 is:
■ sqrt[(p1(1-p1)/n1) +(p2(1-p2)/n2)]
○ The difference between the proportions the standard error = the summation of
the both variances not the sum but based on principle you are combining the
standard error of 2 proportions to give us the overall SE
○ SE = standard deviation of that proportion/statistic
● CLT for phat1 - phat2:
○ If n is sufficiently large:
■ (Phat1 - phat2) ~N(p1-p2, sqrt[(p1(1-p1)/n1) +(p2(1-p2)/n2)])
○ A normal distribution is a good approximation as long as n1p1 > or equal to 10,
n1(1-p1) > or equal to 10, n2p2 > or equal to 10, n2(1-p2) > or equal to 10
find more resources at oneclass.com
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Document Summary
Two proportions: there are two separate categorical variables. One proportion: there is only one categorical variable. You want to compare the proportion of students who use a windows- based pc to the proportion who use a mac. Inference for one proportion since there is only one categorical variable (type of computer used) You want to compare the proportion of students who study abroad between those attending public universities and those at private universities. Inference of two proportions since you have two categorical variables (students abroad and attending public or private universities) You want to compare the proportion of in-state students at a university to the proportion from outside the state. Inference of one proportion since you have one categorical variable (in or out of state) You want to compare the proportion of in-state students who get financial aid to the proportion of out-of-state students who get financial aid.
