A local emergency department would like to estimate the proportion of their patients
attending for back pain who have used over the counter medications (e.g. paracetamol) to
manage their pain before attending. The doctors in the emergency department believe that
10% of these patients may have used these medications before attending.
You were asked to advise on the sampling scheme and calculate the sample size, knowing that
the patients will be sampled as they arrive at the emergency department and you need to
estimate the proportion to within 30% (relative difference) of the true value, with 95%
confidence. It is estimated that 5,000 patients are treated in one year. There are two options
available to select the patients. Either to take a random sample of the patients as they arrive at
the emergency department or survey every k
th patient as they arrive.

(a) Estimate the sample size they would need for systematic sampling and explain exactly
how to obtain one systematic sample of this size of patients.
(4 marks)
(b) Explain the most important advantage and one disadvantage of taking more than one
systematic sample for this study and describe how this would best be done here.
(3 marks)
(c) Explain to the doctors in the emergency department exactly how they could take a
simple random sample for this survey, and the size of sample required.
(2 marks)
systematic sampling versus simple random sampling for this survey. (3 marks)
(Total: 12 marks)
A local health district has conducted a survey of staff at three hospitals to determine their
knowledge of hygiene policies. The survey contained 50 knowledge questions and each
respondent received a score from 0 to 50 with higher scores indicating greater knowledge.
The survey design was a stratified random sample with six strata defined by hospital (A, B
and C) and occupation (doctor and nurse). The number of staff currently employed in each
stratum is given below
Occupation Hospital Number of staff
Nurse A 210
B 250
C 190
Doctor A 45
B 65
C 55
The local health district surveyed 20 participants from each stratum.

Sample Solution