MTH 1210 Biostatistics
Apr 28’09
Homework #14
(
Hypothesis Testing for the Difference between Two Population Means
)
See the handouts #
15, 15a, 15b.
Use
the
MS
Excel
program
Hypothesis_Testing_for_ the_Difference_between_Two_Population_Means.xls.
Solving the problems remember that
what we hope or expect to be able to conclude
as a result of the hypothesis testing usually should be placed in the
alternative
hypothesis H
A
.
Formulate at first the alternative hypothesis
H
A
and then the
null
hypothesis
H
0
which should be
complementary
to
H
A
. Then, choose the proper sheet and
block of cells in the aforementioned Excel program
that correspond to your hypotheses
H
0
and
H
A
and enter the data only in the data entry cells belonging to the
B

column.
In the problems below assume that unknown population variances are
equal
.
7.3.1
(pg. 244 of the textbook) Subjects in a certain study included a sample of
40
men
who claimed to engage in a variety of sports activities (multisport). The mean Body Mass
Index (BMI) for these men was
22.41
with a standard deviation of
1.27
. A sample of
24
male rugby players had a mean BMI of
27.75
with a standard deviation of
2.64
. Is this
sufficient evidence for one to clam that, in general, rugby players have a higher BMI than
the multisport men? Let
α = 0.01.
SAMPLE 1
Size
n
1
=
24
The mean
x
mean_1
*
=
27.7
5
ONEsided test
Std. deviation
s
1
=
2.64
HYPOTHESES
SAMPLE 2
Size
n
2
=
40
H
0
:
µ
1
– µ
2
≤
0
Null hypothesis
The mean
x
mean_2
*
=
22.4
1
Std. deviation
s
2
=
1.27
H
A
: µ
1
– µ
2
>
0
Alternative hypothesis
Hypothesized value of (µ
1
– µ
2
)
0
=
0
df = n
1
+ n
2
– 2 =
62
Level of significance
α =
0.01
t
(1 – α)
=
2.3880
1
<== critical value at
the
upper right
tail
of the curve f(t)
s
p
2
= [(n
1
– 1)s
1
2
+ (n
2
– 1)s
2
2
]/(n
1
+
n
2
– 2) =
3.60006
Test statistic
t
*
= [(x
mean_1
*
– x
mean_2
*
) – (µ
1
– µ
2
)
0
]/(s
p
2
/n
1
+ s
p
2
/n
2
)
1/2
=
10.9001
1
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View Full DocumentREJECT
H
0
BECAUSE
t
*
=
10.9001
>
2.3880
1
= t
(1 – α)
{Students
should
follow
their
textbook
pg.
235
and
the
Excel
program
Hypothesis_Testing_for_the_Difference_between_Two_Population_Means.xls,
sheet
2,
lowest block of cells}
7.3.7
(pg. 247 of the textbook) Cortisol level determinations were made on two samples
of women at childbirth. Group 1 subjects underwent emergency cesarean section
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 Spring '05
 Kzaer
 Statistics, Biostatistics, Standard Deviation, Null hypothesis, Statistical hypothesis testing, std. deviation

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