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AMS 7, Biostatistics
Week 7 Homework Solutions
1. Big decrease in phosphate levels due to new laws?
First determine if the variances are equal:
H
0
:
σ
2
2
=
σ
2
1
, and
H
a
:
σ
2
1
6
=
σ
2
1
.
The
F
statistic
s
2
2
/s
2
1
= 2
.
7.
Using the
F
 distribution with
v
1
= 11 and
v
2
= 9 degrees of
freedom gives the critical value
F
0
.
975
= 3
.
96 leading the conclusion that there is not enough
evidence to reject
H
0
. So, treat the variances as equal (
σ
2
2
=
σ
2
1
) when testing the twosample
hypothesis for the means:
H
0
:
μ
1
≤
μ
2
, and
H
0
:
μ
1
> μ
2
. Calculate
s
2
p
= 1238
.
4 and test
statistic
t
= 9
.
78, and use a
t
distribution with 20 degrees of freedom and obtain a critical
value of
t
0
.
95
= 1
.
725 and thus reject
H
0
.
3. Paired data for antibiotic eFects.
Subtract the amoxicillin column from the penicillin column and get (
n
d
= 6) di±erences
d
= 6
,

10
,
4
,
5
,

7
,

2
and calculate
¯
X
d
=

2
,
¯
s
2
d
= 4
.
12. Test
H
0
=
μ
d
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This note was uploaded on 01/31/2010 for the course AMS 7 taught by Professor Prado,r during the Winter '08 term at University of California, Santa Cruz.
 Winter '08
 Prado,R
 Statistics, Biostatistics, Variance

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