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Sample Problems
Statstics 517
1. In a contingency table, 1000 individuals are classiﬁed by gender and by whether they
favor, oppose, or have no opinion on a complete ban on smoking in public places. The
data is the following.
Smoking in Public Places
Favor
Oppose
No Opinion
Totals
Male
258
228
10
496
Female
297
202
5
504
555
430
15
1000
(a) Test the null hypothesis that gender and opinion on smoking in public places are
independent at
α
=0
.
1. Interpret the result in plain English.
(b) What is the approximate
p
value of the above test?
Chisquare percentiles,
χ
2
df , α
χ
2
2
,
0
.
1
χ
2
2
,
0
.
05
χ
2
2
,
0
.
01
χ
2
6
,
0
.
1
χ
2
6
,
0
.
05
χ
2
6
,
0
.
01
4.60517
5.991465
9.21034
10.64464
12.59159
16.81189
2. Let
X
1
,
···
,X
n
be a random sample from a geometric distribution with paramater
θ
,
i.e.,
f
(
x
;
θ
)=
θ
(1

θ
)
x
,x
,
1
,
2
,
,
0
<θ<
1
You may consider
X
as the number of failures before we see the ﬁrst success in a series
of independent Bernoulli experiments. The success probability for each trial is
θ
.
1
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View Full Document In (a) and (b) below, you may use the fact that the pdf of
Y
=
∑
n
i
=1
X
i
is
g
(
y
;
θ
)=
Pr
(
Y
=
y
±
n
+
y

1
n

1
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This note was uploaded on 09/10/2009 for the course STATS 517 taught by Professor Song during the Fall '07 term at Purdue UniversityWest Lafayette.
 Fall '07
 Song

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