112 what are the upper and lower bounds of the 95 ci

1.12 What are the upper and lower bounds of
the 95% CI for ?̂ (expressed now as a
percent)
1.13 Is the election outcome for Cameron’s
party in the 95% CI?
no
1.14 What statistical principle is this an
example of?

Practice Final 3
Problem 2 Confidence Intervals
Match the margin of error to the desired CI.
Desired CI Answer
Margin of Error
2.1 95% CI for a mean, 𝜎
known
5
1. ?
0.975
(?) ∗ (?√
1
?
+
(?−?̅)
2
∑(?
𝑖
−?̅) 2
)
2.2 80% CI for 2-sample
difference in means,
pooled variance
3
2. ?
0.9
(?) ∗ (√
?
1
2
?
1
+
?
2
2
?
2
)
2.3 80% CI for 2-sample
difference in means,
unpooled variance
2 3. ?
0.9
(?) ∗ (?
?
√
1
?
1
+
1
?
2
)
2.4 95% prediction interval
for ? ̂|?
4 4. ?
0.975
(?) ∗ (?√1 +
1
?
+
(?−?̅)
2
∑(?
𝑖
−?̅)
2
)
2.5 95% CI for ?̂
?
|?
1 5. ?
0.975
∗ (
𝜎
𝑋
√?
)

Practice Final 4
Problem 3.
Hypothesis tests
3.1 Suppose we want to test the hypothesis
0
: 0 vs. : 0
a
H H    
𝜎 unknown and N =50.
If we want
05 . 0  
We would reject the null when:
1.
0.975
(49)
( )
x
t
SE x

2.
05 . 0
) (
z
x SE
x

3.
0.95
(50)
( )
x
t
SE x

4.
0.95
(49)
( )
x
t
SE x

3.2 Suppose we want to test the hypothesis
0
: 0 vs. : 0
a
H H     ,
𝜎 unknown and N =100.
If we want
05 . 0  
We would reject the null when:
1.
0.95
(100)
( )
x
t
SE x

2.
0.90
(100)
( )
x
t
SE x

3.
0.05
(99)
( )
x
t
SE x

4.
0.975
(99)
( )
x
t
SE x

3.3 Suppose we want to test the hypothesis
0 :
1 0
  H , vs
1
: 0
a
H  
N=500
If we want
01 . 0  
We would reject the null when:
1.
1
0.99
1
(499)
( )
b
t
SE b

2.
1
0.99
1
(500)
( )
b
t
SE b

3.
1
0.995
1
(498)
( )
b
t
SE b

4.
99 . 0
1
1
) (
z
b SE
b

3.4 Suppose we want to test the hypothesis
0 :
1 0
  H
, vs
1
: 0
a
H  
N=500
If we want
01 . 0  
We would FAIL TO reject the null when:
1. 1
0.99
1
(500)
( )
b
t
SE b

2.
1
0.01
1
(498)
( )
b
t
SE b

3.
1
0.99
1
(499)
( )
b
t
SE b

4.
1
0.95
1
( )
b
z
SE b


Practice Final 5
Problem 4. Inference for proportions
The Department of Statistics estimates that 50% of students at the University of Washington will have taken
STAT 311 by the time they graduate. You believe it is less than 50%, and decide to take a survey of graduating
seniors to estimate the true proportion. Your friend gets you a list of the graduating seniors and their email
addresses, and you randomly select a sample of n=200, email them, and ask them to report on a Catalyst
survey whether they have taken STAT 311: 40% of seniors report that they have.
Set up a 90% CI for the estimated proportion of seniors who have taken STAT 311.
4.1 Symbolic representation:
?̂ ± ?
𝛼/2
∗ √
?̂ (1−?̂)
?
or ? = ± ?
𝛼/2
∗ √
?̂ (1−? ̂)
?
4.2 With plug-in values:
0.40 ± 1.64 ∗ √
0.4(1−0.4)
200
= 0.40 ± 0.06 or [0.34, 0.46]
State the null and the general alternative hypotheses. What is the approximate distribution of the sample
proportion under the null hypothesis?