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Math 2200
Take Home Quiz
Due Tuesday April 11
th
at the start of class
For each problem: Identify the type of test, write out the null and alternative hypothesis, and include a statement along
with your decision.
1.
Marine engines, particularly those of
large container or cargo ships, are rated to burn fuel based on its viscosity.
The most common fuel is known as 6 oil and should have a kinematic viscosity of 15 mm/s
2
at 100
o
C. Jonny ran
a set of 12 samples of 6 oil from a shore tank and calculated the
mean
viscosity as 14.3 mm/s
2
with a standard
deviation of
1.2
mm/s
2
.
Can Jonny conclude at 99% confidence that the shore tank of 6 oil
is
off spec
? Assume
the distribution is approximately normal.
2.
Gasoline retailers are mandated by the EPA to
have completely transitioned to selling summer
-
grade gasoline by
June 1
st
every year. To be considered summer
-
grade, the Reid Vapor Pressure (RVP)
of the gasoline
can be no
more than 9
psi
.
Enmark
et
is under suspicion of selling winter grade gas past the
June 1
st
deadline. An
investigator pulls
3
0 samples of gas from various Enmark
et
locations and the mean RVP is found to be
9.49
psi.
If the standard deviation of the test method is known to be
0
.
75
psi, can the investigator conclude that they are
sellin
g the wrong grade?
3.
The rumor among gasoline chemists is that
Russia
n oil/gas is very low quality and
Russi
an
boats are rejected
more often than others.
A
s
a
single barge of gasoline can be worth
$
7
-
10 million dollar
s
,
ships are
rarely
rejected
(assume no more than 15% of the time)
.
Shamgan was bored one day while waiting for the cargo boat
to arrive and decided to check the old laboratory records.
In the last
3
years a total of
38
gasoline ships
originated from Russia
. Of those
,
7
failed
their chemical testing
and were rejected
.
At a significance level of
95%, can Shamgan safely conclude that
Russian gas is more likely to
be rejected than
other
gas
?
