24.1 Collecting data, sampling and questionnaires — Practise

1. A sample of 40 pupils includes 12 who walk. Work out the sample proportion who walk.

Answer: The sample proportion is $12/40=3/10$.

2. A random sample of 30 people has 9 who use the bus. Estimate the number in a population of 500 who use the bus.

Answer: Estimate: $150$.

3. In a sample of 80 pupils, 28 bring lunch from home. Work out the percentage.

Answer: $35\%$.

4. A neutral survey records 14 “walk”, 18 “bus”, and 8 “car” responses. How many responses were recorded?

Answer: There were 40 responses.

5. A sample of 25 pupils includes 10 cyclists. Write the sample fraction in its simplest form.

Answer: The sample fraction is $2/5$.

6. A sample of 45 households has 18 with a pet. Estimate the number with a pet in 300 households.

Answer: Estimate: 120 households.

7. A pupil asks only friends from the chess club whether the school should buy more footballs. Work out the percentage represented by 6 yes votes in a sample of 10, and explain one limitation of the sample.

Answer: The sample result is $60\%$. The sample may be biased because chess-club friends may not represent the whole school.

8. A town survey asks 50 people at a train station about car ownership. Work out the percentage represented by 20 car owners, then state one group that may be under-represented.

Answer: $40\%$ own cars in the sample. People who do not use the train station may be under-represented.

9. Replace “You agree that the new route is safer, do you not?” with a neutral question. In a sample of 30 responses, 18 people answer yes. Work out this percentage.

Answer: For example: “Do you think the new route is safe?” The sample percentage is $60\%$.