1.
Suppose that you want to test the hypotheses
H
0:
m
= 100 and
H
1:
m
> 100.
a)
What type of test is it? Right-tailed, left-tailed or two-tailed (
1 point
)?
Right tailed
b)
What is the critical value if you use
a
= 0.01 for a large normal distribution (
1 point
)?
-2.58 and +2.58
c)
What is the critical value if you use
a
= 0.05 for a large normal distribution (
1 point
)?
-1.96 and +1.96
d)
Conduct the hypothesis test using
= 105,
s
= 30,
n
= 100, and
a
= 0.10. What can you conclude (
2 points
)?
e)
What would be your conclusion using a significance level of
a
= 0.01 (
2 points
)?
f)
Conduct the same hypothesis test with
n
= 10, using a 0.01 significance level. What can you conclude (
2 points
)?
2.
A crime reconstruction expert is asked to evaluate the corrosion of a coating of a pipe recovered from the ocean nearby the crime scene and suspected to having been used as a weapon. According to the circumstances of the case, the expert judges relevant to test the corrosion for two coating formulations (referred as Type 1 and Type 2). He obtains eight pipes and paints them half with Type 1 and half with Type 2. Each pipe is then exposed to salt environment for 120 hrs. He then measures the corrosion loss (in
m) for each formulation type on each pipe. The results are reported in the following table:
Pipe
|
Type 1
|
Type 2
|
1
|
197
|
204
|
2
|
161
|
182
|
3
|
144
|
140
|
4
|
162
|
178
|
5
|
185
|
183
|
6
|
154
|
163
|
7
|
136
|
156
|
8
|
130
|
143
|
a)
How do you evaluate the p-value (3 points)?
b)
Can the expert conclude that the mean amount of corrosion differs between the two formulations (
2 points
)?
3.
In the context of a homicide investigation, 12 glitter particles have been recovered from the victim’s garments. As part of an endeavor to offer investigative leads, and specifically to determine the brand of these particles, a forensic scientist has conducted measurements to calculate the surface of these particles. The calculated values of the surfaces are reported in the table below:
|
Glitter particles recovered on victim’s garments
|
Particle #
|
Area (
m2)
|
1
|
6699
|
2
|
6640
|
3
|
6748
|
4
|
6676
|
5
|
6725
|
6
|
6669
|
7
|
6689
|
8
|
6635
|
9
|
6659
|
10
|
6798
|
11
|
6597
|
12
|
6632
|
a)
Calculate the mean estimate and the uncertainty in the form of a 95% confidence interval (3 points).
b)
Report your findings using a formal statement (2 points).
4.
Consider the following example. An experienced forensic toxicologist tests the abilities of two trainees (A and B) to perform determinations of blood alcohol concentrations (BAC) on an external whole blood control sample reported to containing 0.08 g/dL ethanol. Their results are reported in the following table:
n
|
Trainee A
|
Trainee B
|
Examiner
|
1
|
0.067
|
0.070
|
0.081
|
2
|
0.075
|
0.075
|
0.080
|
3
|
0.088
|
0.079
|
0.079
|
4
|
0.082
|
0.071
|
0.078
|
5
|
0.078
|
0.073
|
0.078
|
6
|
0.085
|
0.075
|
0.083
|
7
|
0.072
|
0.070
|
0.078
|
8
|
0.085
|
0.072
|
0.078
|
9
|
0.080
|
0.078
|
0.080
|
10
|
0.092
|
0.069
|
0.069
|
While evaluating the results, the examiner was not expecting to observe values under 0.070 g/dL and suspects that all the values under 0.070 g/dL are outliers. He asks you to perform a formal statistical analysis to verify if there are aberrant values at
α
=0.05 that can be removed from the datasets.
a)
Has the Examiner collected outlier values that should be rejected (2 points)?
b)
Has Trainee A collected outlier values that should be rejected (2 points)?
c)
Has Trainee B collected outlier values that should be rejected (2 points)?