### Inference Review I

```AP Statistics
Inference Review
Chapters 18-25
1 Proportion:
CI =
pˆ  z
1 Sample or Matched Pairs t-test
pˆ qˆ
n
CI = x  t
Hypothesis Test: z =
pˆ  p
pq
n
2 Proportion:
CI =
( pˆ 1  pˆ 2 )  z
Hypothesis Test:
df
s
n
Hypothesis Test:
x
tdf = s
n
2 Sample t-test:
pˆ 1qˆ1 pˆ 2 qˆ 2

n1
n2
( pˆ1  pˆ 2 )  0
z = p pool q pool  p pool q pool
n1
n2
CI:
( x1  x2 )  t df
s12 s22

n1 n2
Hypothesis Test: tdf =
( x1  x2 )  0
s12 s22

n1 n2
Remember PANIC for CI’s and
PHANTOMS for Hypothesis Tests
Parameter
Assumption
Name Test and Statistics
Interval (Include Formula)
Conclusion
Parameter
Hypothesis (p or mu)
Assumptions/Conditions
Name Test
Test Statistics
Obtain P (Include formula and distribution)
Make Decision (Never accept Ho
State Conclusion (In Context)
Name Statistics: n = 50, p-hat = .7, q-hat = .3
Interval:
CI  .7  1.96
Conclusion:
(.7)(.3)
50
Parameter: p = proportion of city workers who are also in the union
Hypothesis:
Independent: Each person being in
The union should be independent
Name: One proportion z-test
Test Statistics: p-hat = .12, p = .135, q = .865, n = 2000
Obtain P:
z
Decision:
Conclusion:
.12  .135
(.135)(.865)
2000
Parameter:
Assumptions:
Name: 2 Proportion z-Interval
Interval:
CI  (.065 .017)  2.576
Conclusion:
(.065)(.935) (.017)(.983)

1000
1000
Parameter: Ps = Proportion of suburban students that failed AP exam
Pr = Proportion of rural students that failed AP exam
Hypothesis: Ho: Ps = Pr, Ha: Ps ≠ Pr
Assumptions:
10%: Both 107 and 143 are less than 10%
of rural and suburban students that took
AP exam.
Name:
2 Proportion z-test
Make Decision:
Fail to reject Ho
Test Statistics:
State Conclusion:
Obtain P:
z
(.280 .315)  0
 .59
(.3)(.7) (.3)(.7)

107
143
P =.56
Parameter:
Name Test:
Interval:
Assumptions:
Random: It is a random selection of days
during the year.
Nearly Normal: The histogram is roughly
unimodal and symmetric
Independent: Each car’s speed should
be independent
10%: 20 cars is less than 10% of all cars
that pass through when the sign is flashing
CI  24.6  t19
7.24
20
Conclusion:
Parameter: U = average # of hours students watch TV per week from Central High
Hypothesis: Ho: U = 13, Ha: U > 13
Assumptions:
Name Test:
Test Statistics:
Obtain P:
Nearly Normal: Histogram is roughly unimodal
and symmetric.
Random: Students were randomly selected
Independent: TV watching among students
should be independent
10%: 25 students is less than 25% of all students
at CHS.
Conclusion:
Parameter:
Assumptions:
Name:
Interval:
CI  (15.625 14)  2.131
Conclusion:
3.122 2.532

16
16
Parameter: Um = mean death age of men, Uw = mean death age of women
Hypothesis: Ho: Um = Uw, Ha: Um < Uw
Assumptions:
Name Test:
Test Statistics:
Obtain P:
t71.8 
(68.33  78.7)  0
12.492 16.432

48
40
Conclusion:
Parameter: Ud = The mean difference in unemployment rate between Australia and UK
Assumptions:
Assumptions continued:
Nearly Normal: Histogram is roughly
unimodal and symmetric
10%: 1990 – 2000 represents less than 10% of
All of the years
Name:
Interval:
Conclusion:
Parameter: Ud = The mean difference in employment rate between Males and Females
Hypothesis:
Assumptions:
Name:
Match paired t-test
Test Statistics:
Obtain P:
t7 
346.125 0
713.166
8
Make Decision: Fail to reject Ho
State Conclusion:
```