ap statistics. has been about the distribution of sample means and the distribution of the...
TRANSCRIPT
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.