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Solutions  Comparing Two Groups
10.1 Wealth gap:
a) The response variable is net worth and the explanatory variable is race.
b) The two groups that are the categories of the explanatory variable are white and black
households.
c) The samples of white and black households were independent. No household could
be in both samples.
10.2 Sampling sleep
:
a) The samples on weekdays and weekends should be treated as dependent samples
because every person is in both samples.
b) When compared with other people from another year, the samples should be treated
as independent. No one person is in both samples.
10.3 Binge drinking:
a) The estimated difference between the population proportions in 2005 and 1993 is
0.07. The proportion of students who reported bingeing at least 3 times within the
past 2 weeks has apparently increased between 1993 and 2005.
b)
The standard error is the standard deviation of the sampling distribution of
differences between the sample proportions.
se
=
(
29
(
29
2
2
2
1
1
1
ˆ
1
ˆ
ˆ
1
ˆ
n
p
p
n
p
p

+

=
(
29 (
29
(
29 (
29
485
382
.
0
1
382
.
0
159
312
.
0
1
312
.
0

+

=0.0429
c) 0.07 – (1.96)(0.0429) = 0.01
0.07 + (1.96)(0.0429) = 0.15
(0.01, 0.15)
We can be 95% confident that the population mean change in proportion is between 
0.01 and 0.15. This confidence interval contains zero; thus, we do not have enough
evidence to conclude that there was an increase in the population proportion of UW
students who reported binge drinking at least 3 times in the past 2 weeks between
1993 and 2005.
d)
The assumptions are that the data are categorical (reported binge drinking at least
3 times in the past 2 weeks vs. did not), that the samples are independent and are
obtained randomly, and that there are sufficiently large sample sizes. Specifically,
each sample should have at least ten “successes” and ten “failures.”
10.11 Hormone therapy for menopause
:
a) Assumptions: Each sample must have at least ten outcomes of each type. The data
must be categorical, and the samples must be independent random samples.
Notation:
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 '08
 BARROSO,JOAOR
 Statistics

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