BN001, BN009 Mathematics 4
Hypothesis Testing
Worksheet 1
Question 1
The manufacturers of a components are claiming that the mean
lifetime of
the component, when tested to destruction, is 6.7 x 105 seconds.
A batch of
70 units were tested to destruction and their lifetimes
recorded. Test the
manufacturers claim with an appropriate hypothesis test, with a
level of
significance of 0.01. The lifetimes Li are listed here in units
of 104
s.
65.08 71.33 63.48 65.64 70.33 68.33 70.44
68.74 64.22 63.96 66.6 68.36 72.23 72.64
68.42 67.3 72.44 65.7 69.91 70.14 70.16
72.99 68.45 69.66 63.47 64.53 67.46 71.17
65.13 68.38 68.26 67.81 66.76 68.84 64.54
67.92 67.98 65.95 67.91 70.6 65.21 71.78
64.81 70.93 68.31 65.95 71.06 63.55 63.34
71.36 66.35 66.69 66.85 67.81 70.44 65.84
72.14 66.61 69.79 68.84 67.44 71.75 66.17
68.43 68.24 72.48 71.07 65.82 63.01 70.26
Hint: The variable involved here is:
ns
xz
.
Question 2
A milling machine is producing circular disks of metal. The
diameter was
recorded, in millimetres, of a large number of disks produced on
one day.
It is claimed that the true mean of the diameters is 48mm. Test
this
hypothesis using an appropriate statistic, with a level of
significance of
0.05. The diameters Di are listed here:
42.60 54.87 54.93 50.07 40.91 47.50 43.10 45.41 45.93
43.66 52.34 44.32 52.99 56.58 40.76 49.70 40.97 56.80
59.87 46.81 47.92 59.22 41.29 56.43 40.83 49.27 46.76
44.45 47.58 40.09 57.19 62.95 44.95 45.51 45.43 61.40
41.32 41.67 40.30 49.51 45.63 48.64.
Question 3
Repeat the test in Question 2 using the values listed below make
a note
of the difference this makes to your test.
44.60 52.87 51.93 50.07 47.91 47.50 46.10 45.41
45.93 47.66 50.34 47.32 52.19 50.58 44.76 49.70
Hint: The variable involved here is:
ns
Dt
.
Question 4
A claim has been made in a national newspaper that the mean
salary of
Computer engineers, five years after graduation, is 58,000 or
higher. The
following data was collected to investigate this claim; it
consists of the
salaries of 15 people in this position, in thousands of
euro.
51.7 53.6 50.1 57.3
60.6 55.0 52.3 51.2
44.1 51.7 53.4 53.2
56.8 56.0 61.1
Test the claim that the starting salaries are 58K or higher.
Question 5
A weather station has recorded daily rainfall amounts at a
particular
location on the east coast of Ireland. The amounts are listed
here,
measured in millilitres (ml):
729 693 723 705 704 695
717 740 736 721 717 693
711 716 718 750 760 708
Carry out a test to see if this data supports a claim that the
mean rainfall
for this region is at most 700ml.
Question 6
It is claimed that drinking certain types of yogurt drinks
lowers blood
cholesterol levels. A trial was run to test this with 10
individuals. For each
person, their cholesterol level was measured. They then consumed
the
yogurt drink for one year, after which their cholesterol level
was measured
again. The values are given in the table below. Carry out an
appropriate
test to determine whether the cholesterol levels have
fallen.
Before 5.22 4.59 5.74 4.29 5.82 5.69 5.61 6.10 5.56 5.34
After 4.21 4.88 5.75 5.34 5.73 4.91 5.56 4.80 5.72 5.12
Hint: The variable involved is:
n
s
Dt
D
D , where D is the difference.
Question 7
It is suspected that a treatment on the moving parts of an
engine change
the coefficient of friction of those parts. For a set of ten
engines, the
coefficient was measured firstly without the treatment, then
measured a
second time with the treatment. The values are given in the
table below.
Carry out an appropriate test to determine whether the whether
the
coefficient has increased.
With 15.22 14.59 14.83 14.29 14.93
Without 14.25 14.23 14.82 14.34 14.14
With 15.69 14.61 14.1 15.56 15.34
Without 15.91 14.56 13.8 14.72 15.42
