A researcher numbers all 250 members of a gym from 1 to 250 and uses a random number generator to select 20 members, so that every member has an equal chance of being chosen. Name this sampling method.
(Total for Question 1 is 1 mark)
2
A quality inspector checks every 25th item that comes off a production line. Name this sampling method.
(Total for Question 2 is 1 mark)
3
A market researcher stands outside a train station and asks the first 30 people who walk past to complete a survey. Name this sampling method.
(Total for Question 3 is 1 mark)
4
Write down whether the following statement is True or False. A sampling frame is a list of every member of the population from which a sample can be drawn.
(Total for Question 4 is 1 mark)
5
A list contains 360 names. A systematic sample of size 24 is needed. Work out the sampling interval.
(Total for Question 5 is 2 marks)
6
A college has 840 students: 360 study Arts and 480 study Science. A sample of 70 students is taken, stratified by subject. Work out the number of Science students that should be sampled.
(Total for Question 6 is 2 marks)
7
A town has a population of 5400 people split into three age groups: 0-17 (1200), 18-64 (3300), 65+ (900). A stratified sample of size 90 is taken. Work out how many people aged 65+ should be in the sample.
(Total for Question 7 is 2 marks)
8
A charity has 240 volunteers. A simple random sample of 15 volunteers is chosen so that every volunteer has an equal chance of selection. Work out the probability that a particular volunteer, Aisha, is chosen.
(Total for Question 8 is 2 marks)
9
A list of 500 items is numbered 1 to 500. A systematic sample of 20 items is needed, and the first item selected at random is item 9. Work out the sampling interval, and write down the number of the third item selected.
(Total for Question 9 is 2 marks)
10
In a stratified sample of a school with 1000 students, 45 of the 300 Year 11 students were sampled. Using the same sampling fraction, work out how many of the 260 Year 10 students should be sampled.
(Total for Question 10 is 2 marks)
11
A researcher wants a sample of 20 men aged 30 to 40 and 20 women aged 30 to 40 from shoppers at a mall. She stops shoppers and interviews them until each group of 20 is filled. State the sampling method used, and give one reason it might introduce bias.
(Total for Question 11 is 2 marks)
12
Write down whether the following statement is True or False. In systematic sampling, the sampling interval is found by dividing the population size by the desired sample size.
(Total for Question 12 is 1 mark)
13
A biologist divides a lake into 4 zones and chooses 2 zones at random, then records every fish caught within those 2 zones. Name this sampling method.
(Total for Question 13 is 1 mark)
14
A youth orchestra has 54 string players and 36 wind players, 90 players in total. A sample of 30 players is taken, stratified by section. Work out how many string players and how many wind players should be sampled.
(Total for Question 14 is 2 marks)
15
A hospital has three wards: Ward A (48 patients), Ward B (72 patients) and Ward C (60 patients), 180 patients in total. A researcher takes a stratified sample of 45 patients across the wards. Work out the number of patients that should be sampled from each ward.
(Total for Question 15 is 3 marks)
16
A company has 280 employees, numbered 1 to 280 in a list. A systematic sample of 14 employees is needed, with a random starting point of 3. Work out the sampling interval, and list the first five employee numbers that will be selected.
(Total for Question 16 is 3 marks)
17
A school wants to find out students' opinions on a new lunch menu. The head teacher surveys the first 30 students to arrive at school each day for a week. (a) Give a reason why this sample might not be representative of the whole school. (b) Suggest a more appropriate method to select a representative sample of 30 students from the school's 900 students, giving one advantage of your method.
(Total for Question 17 is 3 marks)
18
A company has 800 employees: 320 in Sales and 480 in Operations. In a stratified sample, 24 employees were selected from the Sales department. Using the same sampling fraction, work out the total number of employees that should be selected from all 800 employees.
(Total for Question 18 is 3 marks)
19
A factory produces 630 items per shift, numbered 1 to 630 in the order they are made. A quality controller uses systematic sampling to inspect 1 in every 30 items, with a random starting point between 1 and 30. (a) Work out how many items will be inspected during one shift. (b) Work out the probability that the random starting point is exactly 1.
(Total for Question 19 is 3 marks)
20
A gym has three types of membership: Standard (600 members), Premium (150 members) and Family (250 members), 1000 members in total. A stratified sample of 40 members is required. (a) Work out how many Premium members should be sampled. (b) Give one reason why stratified sampling is more appropriate than simple random sampling in this situation.
(Total for Question 20 is 3 marks)
Mark scheme · S06D Sampling Methods: Fluency and Exam Drill
Question 1
B1 Simple random sampling cao
Answer: Simple random sampling
Question 2
B1 Systematic sampling cao
Answer: Systematic sampling
Question 3
B1 Convenience sampling (or opportunity sampling) cao
Answer: Convenience (opportunity) sampling
Question 4
B1 True cao
Answer: True
Question 5
M1 correct method, 360 divided by 24
A1 15 cao
Answer: 15
Question 6
M1 correct method, (480/840) x 70
A1 40 cao
Answer: 40
Question 7
M1 correct method, (900/5400) x 90
A1 15 cao
Answer: 15
Question 8
M1 correct method, 15/240
A1 1/16 oe (0.0625) cao
Answer: 1/16 (0.0625)
Question 9
M1 correct interval, 500/20 = 25, and 9 + 2 x 25 used
M1 fraction applied correctly to at least two wards
A1 Ward A: 12, Ward B: 18, Ward C: 15, all cao
Answer: Ward A: 12, Ward B: 18, Ward C: 15
Question 16
M1 correct interval, 280/14 = 20
M1 correct method to build the list, starting number plus repeated interval
A1 3, 23, 43, 63, 83 all cao
Answer: Interval = 20; first five numbers: 3, 23, 43, 63, 83
Question 17
B1 valid reason, e.g. students who arrive early may not represent all year groups or travel habits oe
B1 valid named method, e.g. simple random sampling using a numbered list of all 900 students oe
B1 valid advantage of the named method, e.g. every student has an equal chance of being chosen, reducing bias oe
Answer: (a) Early arrivals may not represent the whole school, e.g. by year group or how they travel to school. (b) Number all 900 students and use simple random sampling; every student then has an equal chance of selection, which reduces bias.
Question 18
M1 correct sampling fraction found, 24/320 (= 3/40 or 0.075)
M1 fraction applied to the total population, 0.075 x 800
A1 60 cao
Answer: 60
Question 19
M1 correct method, 630/30
A1 21 cao
B1 1/30 oe cao
Answer: (a) 21 items. (b) 1/30
Question 20
M1 correct method, (150/1000) x 40
A1 6 cao
B1 valid reason, e.g. Premium is a small group and could be under-represented or missed entirely in a simple random sample oe
Answer: (a) 6. (b) Stratified sampling ensures the small Premium group is proportionally represented, which a simple random sample might miss.