Practice Final; Statistics 371; Fall 2011; Professor Wardrop
Below are selected values of
t
for Gosset’s 95% intervals. If you cannot Fnd the
t
you need
below, use
z
=1
.
96
.
df:
6
7
8
9
10
11
12
13
14
15
t
:2
.
4
4
7
2
.
3
6
5
2
.
3
0
6
2
.
2
6
2
2
.
2
2
8
2
.
2
0
1
2
.
1
7
9
2
.
1
6
0
2
.
1
4
5
2
.
1
3
1
df:
16
17
18
19
20
21
22
23
24
25
t
.
1
2
0
2
.
1
1
0
2
.
1
0
1
2
.
0
9
3
2
.
0
8
6
2
.
0
8
0
2
.
0
7
4
2
.
0
6
9
2
.
0
6
4
2
.
0
6
0
Problems 1–2 are about Simpson’s Paradox.
In each problem you are given a collapsed table
and two partially completed component tables
for it. In each of these problems Fnd all pairs
of values of
c
and
d
so that Simpson’s Paradox
is occurring
or
explain why Simpson’s Paradox
cannot
occur for these data. You must present
computations to justify your answer. Make sure
to label which number is
c
and which is
d
.
1. The collapsed table is below.
Group
SF
Total
11
0
2
1
9
8
3
0
0
28
9
1
6
1
2
5
0
191
359
550
The component tables are below.
Subgp A
Subgp B
Gp
Tot
Gp
16
0
1
4
0
2
0
0
14
2
5
8
1
0
0
2
c
100
2
d
150
300
250
2. The collapsed table is below.
Group
7
8
3
1
3
0
24
2
5
8
1
0
0
89
141
230
The component tables are below.
Subgp A
Subgp B
Gp
Gp
12
1
5
47
5
6
2
95
5
2
c
35
2
d
65
110
120
3. In the 1983 Wisconsin Survey of drivers,
40.7% of 450 females responded ‘Ex
tremely serious’ to the question
How serious a problem do you
think drunk driving is in Wis
consin?
In addition, 36.4% of 538 males gave the
same answer to this question.
Compare the implied populations with a
95% conFdence interval. Carefully state
your assumptions.
4. Refer to the previous question. The sub
jects were asked:
If you are arrested for drunken
driving, what are your chances
of being convicted?
Of the 446 females, 17.3% answered ‘very
high;’ of the 537 males 25.7% answered
‘very high.’
Compare the implied populations with an
95% conFdence interval. Carefully state
your assumptions.
1
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View Full Document5. I have drawn a histogram for 500 obser
vations.
One of the rectangles has end
points of 1.00 and 3.00, and a height of
0.20. For each of the three situations be
low, determine
how many
observations are
in this class interval [1.00 to 3.00), with the
usual endpoint convention.
(a) If it is a frequency histogram.
(b) If it is a relative frequency histogram.
(c) If it is a density scale histogram.
6. I have drawn a histogram for 800 obser
vations.
One of the rectangles has end
points of 0.20 and 0.30, and a height of 5.
For each of the three situations below, de
termine
how many
observations are in this
class interval [0.20 to 0.30), with the usual
endpoint convention.
(a) If it is a frequency histogram.
(b) If it is a relative frequency histogram.
(c) If it is a density scale histogram.
7. I observed 50 i.i.d. trials. Below are my 50
sorted observations.
0.02
0.04
0.14
0.18
0.32
0.44
0.46
0.68
0.86
1.04
1.06
1.26
1.32
1.38
1.42
1.50
1.54
1.56
1.60
1.74
2.26
2.40
2.58
2.62
2.72
2.94
3.26
3.38
3.54
3.56
3.76
3.80
3.94
4.34
4.56
5.06
5.50
5.90
6.02
6.08
6.20
6.52
6.84
8.52
8.60
10.00
10.42
10.84
x
(49)
11.86
(a) Draw a density scale histogram of
these data. Use 0.00–2.00, 2.00–6.00,
and 6.00–12.00 as your class inter
vals. Clearly label the height and end
points of each of the rectangles.
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 Fall '11
 hanlon
 Statistics, Regression Analysis, Type I and type II errors, Gosset

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