1
Midterm Exam #1, 2008, Stat 102
–
Solutions
Sections:
001
= M&[email protected]:30;
002
= T&[email protected]:30;
003
= T&[email protected]:30
Instructions
: This is a semi-closed book exam. Up to two pages of notes are allowed. (These
two pages may be two-sided if you wish.)
When performing hypothesis tests, clearly state the null and alternative hypotheses and
show the critical value and/or P-value (from the table) where appropriate.
Normal tables, t tables and F tables are provided, as needed.
Write your answers on the
test and always show your work.
Partial credit will be given.
Time:
90 minutes
.
Your Name ____________________________
Section #: 001 (Prof. Brown) _______
002 (Prof. Zhao)
_______
003 (Prof. Zhao)
_______
Sections:
001
= M&[email protected]:30;
002
= T&[email protected]:30;
003
= T&[email protected]:00
Point Allocations are indicated for each numbered problem (out of 100 total points).

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2
1.
[20 Points]
It is often claimed that blood pressure increases with age. Here is some data
about Systolic Blood Pressure for a sample of females at age 48 and at age 58. Here are the side-
by-side boxplots and summary statistics for the 48 year olds and for the 58 year olds.
100
150
200
250
SBP
48
58
AGE
Age
Number
Mean
Std Dev
Std Err Mean
48
41
142.85
20.48
3.198
58
37
157.14
33.38
5.488
Here is some JMP output for tests of equality of blood pressure among the two age groups:
Assuming equal variances
Difference
14.282
t Ratio
2.302
Std Err Dif
6.204
DF
76
Not Assuming equal variances
Difference
14.282
t Ratio
2.248
Std Err Dif
6.352
DF
58.5
(a)
Conduct a suitable test of the null hypothesis that the two groups have equal mean blood
pressures. Give the (approximate) P-
value of the test. Can you conclude at α = 0.05 that the two
groups have different mean
blood pressures? Can you conclude this to be so at level α = 0.01?
SOLUTION:
Since the larger of the larger ratio of
2
2
2
2
1
2
/
33.38 / 20.48
2.67
3
s
s
, we may
take the equal variance assumption. So the t ratio is 2.3 with df=76. This results in a p-value
of 2*P(Z>2.3)=2*.0107=.02. We will reject the null hypothesis at α = 0.05
but not at α = 0.01.