AP Statistics
Jan 18, 2016
AP Statistics
Has been about the distribution of sample means
and the distribution of the difference of sample means.
and the distribution of sample proportions
1 2
2 21 2
1 2
ˆ
xz
n
xts n
x xt
s s
n n
p pz
pqn
1 2
1 2
1 2
2 21 2
1 2
ˆ
ˆ
x
x
x x
x x
p
p
n
n n
p
pq
n
1 2 1 2
1 2 1 2
1 2
ˆ ˆ ˆ ˆ 1 2
1 1 2 22 2 2ˆ ˆ ˆ ˆ
1 2
1 1 2 2ˆ ˆ
1 2
1 1 2 2
1 1
1 1
Formula for std dev true only if independence
condition is met: pop >10 & pop >10
p p p p
p p p p
p p
p p
p p p p
n n
p p p p
n n
n n
If these conditions are met, the sampling distribution of difference of proportions is approximately normal
1 1
1 1
2 2
2 2
ˆ 5
ˆ 5
ˆ 5
ˆ 5
n p
n q
n p
n q
1 1 2 2
1 2
*1 2
ˆ ˆ ˆ ˆ1 1
ˆ ˆ
p p p pSE
n n
CI p p z SE
Researchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking the medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Construct a 95% confidence interval for the true difference in the proportion of people reporting anxiety on the placebo and drug.
1: Populations & Parameter of Interest
2: Procedure Name & Conditions
3: Calculations
4: Interpret
Two-Proportion Z intervalResearchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking the medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Construct a 95% confidence interval for the true difference in the proportion of people reporting anxiety on the placebo and drug.
1: Population, Parameter of Interest,H0 and Ha
2: Procedure Name & Conditions
3: Calculations
4: Interpret
0 1 2
1 2
1 2
1 2
:
:a
H p p
H
p p
p p
p p
1 2
1 2
1 1 2 2
1 2
ˆ ˆ
1 1ˆ ˆ1
where
ˆ ˆˆ
p pz
p pn n
n p n pp
n n
Two-Proportion Z Test
Researchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking the medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Is the medication working any differently than the placebo? Test this claim at the 5% significance level.v
Two-Proportion Z Test
1: Population, Parameter of Interest,H0 and Ha
2: Procedure Name & Conditions
3: Calculations
4: Interpret
Two-Proportion Z Test
Researchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking the medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Is the medication working any differently than the placebo? Test this claim at the 5% significance level.