Biomedical Engineering Reference
In-Depth Information
(a)
At a given level of risk for a type-I error, what is the ratio of
the minimum significant measured activities for the two
counters?
(b)
It is decided that the acceptable risks for type-I and type-II
errors are both to be 10%. Additional shielding can be
placed around counter 1 to reduce its background. If
nothing else is changed, what number of background
counts,
B
1
, would then be required to achieve a minimum
detectable true activity of 30 Bq?
(c)
What factors determine the value of the calibration
constant?
(d)
What difference does it make in the minimum significant
measured activity and in the minimum detectable true
activity, if the expected number of background counts is not
accurately known?
46.
At a certain facility, one net count corresponds to an activity of
12.9 Bq in a sample; and the expected number, 816, of
background counts is well known.
(a)
If the maximum acceptable risk for making a type-I error is
0.050, what is the minimum significant net count?
(b)
If the minimum detectable true activity is
A
II
=
1300
Bq,
what is the risk of making a type-II error when a sample
has an activity exactly equal to
A
II
? (Use the approximate
formula.)
(c)
What is the probability of making a type-II error in a single
measurement with a sample that has an activity exactly
equal to the minimum significant measured activity?
(d)
If the minimum detectable true activity
A
II
were taken to be
the same as the minimum significant measured activity
A
{
,
what would be the probability of making a type-II error
with a sample having an activity equal to
A
II
?
47.
Repeat Problem 42 with the measured number of background
counts 1080 not accurately known.
48.
Repeat Problem 46(a) and (b) with the measured number of
background counts 816 not accurately known.
49.
Show that Eqs. (11.79) and (11.80) follow from Eq. (11.78).
50.
In a court of law, one judge might tend to be lenient, while
another is a “hanging judge.” With respect to the possible guilt
of a defendant, what relative importance do the two judges
place on not making errors of type-I and type-II?
51.
The resolution of a scintillation counter is 8.2% for 0.662-MeV
gamma photons from
137
Cs. What is its resolution for
1.17-MeV gamma rays from
60
Co?
