Microsoft word - test autumn 2009.doc
MSc Medical Physics, Radiation Detection and Instrumentation, Radiation and
Generic Skills Module Statistics Test Autumn 2009. Prof B N Murdin
Answer either all questions A or all questions B or all questions C.
Questions 1-3 are worth 5 marks each, while Questions 4&5 are worth 10 marks each.
A1. Describe the kind of event that is governed by Binomial statistics
B1. Describe the kind of even that is governed by Poisson statistics
C1 Describe the Central Limit Theorem
A2. A radiation detector is switched on for 5 minutes and measures 2397 counts. What is the count
rate per second and its error?
B2. A new road opens and in the first month there are 3 accidents. What is the accident rate per year
and its error?
C2. A virologist observes 10 cases of Tamiflu-resistant influenza in her North-London clinic
(catchment population 1 million). What is the rate per thousand people and its error?
A3. A clinical trial takes two randomised cohorts and gives a different drug to each. Identify the null
hypothesis (with justification).
B3. Radiation physics laboratory students measure their accumulated dose using portable sensors, and
the doses are read out and compared with students from the previous year. Identify the null hypothesis
C3. The nitrous oxide pollution level readings are taken for a main road in Guildford and compared
with those of a similarly busy road in Redhill. Identify the null hypothesis (with justification). For the next two questions (4&5), assume that the samples are large enough that using Student’s t-
distribution is not necessary.
A4. Blood cholesterol levels were measured in a sample of 9 adult males and the mean and standard
deviation were 4.8 mmol/L and 0.6 mmol/L. A second group of 9 were given a homeopathic
treatment for a month prior to the test, and the mean of 5.2 mmol/L and a standard deviation of 0.8
mmol/L. Are the values significantly different at the 95% level? What is the probability of getting this
data if the treatment in fact makes no difference?
B4. Patients receiving radiotherapy for an aggressive glioma were randomised to receive a new
treatment or the traditional therapy (22 patients per group). Patients with the new therapy including
hyperbaric oxygen and chemotherapy had survival time of 17.5 months and s.d. 7.4 compared with
12.7 months and s.d. 6.4 for the standard therapy. Are the values significantly different at the 95%
level? What is the probability of getting this data if the new treatment is in fact ineffectual?
C4. Solar power researchers developing photovoltaic cells develop a new version. A set of 10 devices
using the new technology had an average efficiency of 23% with s.d. of 2%, while 10 standard cells
prepared under the same conditions had 21% and s.d. 2%. Are the values significantly different at the
95% level? What is the probability of getting this data if the new technology is in fact ineffectual?
A5. Of 40 refrigerators repaired in the Electrelex shop, 8 develop faults within one year, compared
with 1 refrigerator out of 25 repaired by their rival Eluctrulux. What is the probability of post-repair
faults in each case? Are they significantly different at the 95% level?
B5. Of a set of 52 HIV-positive patients, 6 are found to have hepatitis, compared with 1 hepatitis
infection out of 73 who present with influenza. What is the probability of hepatitis infection in each
case? Are the probabilities of hepatitis infection significantly different between the HIV and influenza
groups at the 95% level?
C5. Of 48 coronary bypass patients who presented with normal left ventricular function, 34 survived
for fifteen years or more, while for 59 patients with abnormal left ventricular function, 30 survived the
same time. What is the probability of survival in each case? Are they significantly different at the
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