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Ecolint Campus des NationsMathematics
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Pack A — Fluency

Ecolint Campus des NationsMathematics
Year 8 · 8.10 Sampling

Pack A · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    Distinguish: a (a) survey, (b) census, (c) population, (d) sample. Give one-sentence definitions.
     
  2. 2.
    A school has 600 students. A class of 30 is surveyed. Identify the population and the sample.
     
  3. 3.
    A researcher gives each student a number and uses a random-number generator to pick 30. What sampling method is this?
     
  4. 4.
    A sample of 60 out of 600 pupils is taken. What percentage is the sample of the population?
     
  5. 5.
    In a sample of 25 students, 3 were left-handed. Estimate the number of left-handed students in a school of 500.
     
  6. 6.
    A survey question reads "Do you agree that the canteen serves poor food?" Why is this biased?
     
  7. 7.
    A survey of 100 pet owners finds 65% have dogs. Estimate how many dog owners there are in a community of 800 pet owners.
     
  8. 8.
    A teacher surveys only students who attend the library to ask about reading habits. State one source of bias.
     
  9. 9.
    In a sample of 50 cars, 12 are red. Estimate the percentage of red cars in the population.
     
  10. 10.
    A teacher takes the first 30 students arriving at school as a sample. Identify a potential bias.
     
SilverQuestions 11–20
  1. 11.
    A school has Year 7: 200, Year 8: 180, Year 9: 220. A stratified sample of 60 is to be taken. How many from each year?
     
  2. 12.
    A poll of 200 voters finds 110 support candidate A. Estimate the percentage of supporters in the wider population, and comment on how confident this estimate is.
     
  3. 13.
    A researcher wants to learn about Year 8 lunch preferences. Suggest a sampling plan that avoids bias.
     
  4. 14.
    Identify whether each scenario is a census, a sample or biased: (a) UK government population census every 10 years. (b) Surveying every 10th student exiting the school. (c) Asking the football team about favourite sport.
     
  5. 15.
    A class of 30 students is surveyed about study time. The mean is 7.4 hours/week. Is this representative of all Y8 students? Suggest two reasons it might not be.
     
  6. 16.
    Improve this question: "How often do you eat the disgusting cafeteria food?" Provide a fairer version.
     
  7. 17.
    A sample of 40 students has 18 left-handed. The expected proportion is 10%. Comment on whether the sample is consistent with this.
     
  8. 18.
    A teacher conducts a survey on a school trip. List two reasons why this sample is unlikely to represent the whole school.
     
  9. 19.
    Identify the most representative sampling method for a school survey: (a) volunteers in the library; (b) random class draw; (c) every 10th student exiting; (d) stratified across year-groups.
     
  10. 20.
    A data set has the values 152, 148, 1500, 155 (heights in cm). Clean it and explain.
     
GoldQuestions 21–30
  1. 21.
    A school survey on phone use has 800 students. A stratified random sample of 80 is taken: Year 7 (200), Year 8 (180), Year 9 (220), Year 10 (100), Year 11 (100). How many from each year?
     
  2. 22.
    A sample of 30 students reports an average of 6.5 h homework per week with range 4. Estimate the school-wide average (school of 600 students) and discuss the confidence in this estimate.
     
  3. 23.
    For a survey about lunch preferences in a school of 1000 students, you want results accurate to ±3%. Approximately how large a sample is needed?
     
  4. 24.
    A school surveys 120 students about whether they bring their own lunch. 78 say yes. (a) What percentage in the sample? (b) Estimate the count in a year-group of 600. (c) Comment on accuracy.
     
  5. 25.
    A survey question is "Do you prefer cats over dogs?" State two ways this question is poorly designed and improve it.
     
  6. 26.
    A teacher considers two sampling plans for a school of 600. (i) 60 random students from the whole school; (ii) the first 60 students arriving at school. State which is better and why.
     
  7. 27.
    A doctor wants to estimate the average daily steps for the local town (~50 000 people). Suggest two methods, with pros and cons.
     
  8. 28.
    A school survey contains the question: "How many hours of TV do you watch a week? (a) 0–5, (b) 6–10, (c) 10–15, (d) more than 15." Identify the problem with the response options.
     
  9. 29.
    Sample with replacement vs without replacement. A class of 30 students has names placed in a hat. Five draws are made (with replacement). On average, how many distinct names are drawn?
     
  10. 30.
    In an opinion poll, respondents are asked: "How satisfied are you with the school cafeteria? Very satisfied / Satisfied / Neutral / Dissatisfied / Very dissatisfied." Identify whether this is biased.
     
PlatinumQuestions 31–40
  1. 31.
    A school of 800 students will be surveyed about transport. Year 7: 200, Year 8: 200, Year 9: 200, Year 10: 100, Year 11: 100. A stratified sample of 80 is required, but you want to ensure ≥ 5 from Year 11. How many from each year?
     
  2. 32.
    A sample of 50 dogs at a vet has mean weight 18 kg, range 30 kg. The vet treats 1000 dogs/year. Estimate the population mean and discuss the spread.
     
  3. 33.
    A polling firm surveys 1000 voters and reports candidate A at 51% support. Margin of error ±3%. What does this mean for confidence?
     
  4. 34.
    A pet-owner survey has 60% response rate (out of 500 sent). 200 responded "yes, owns a pet". Estimate the percentage of pet owners in the surveyed population.
     
  5. 35.
    A student conducts a survey at the school gate asking about phone use. Identify three types of bias possible and how to reduce each.
     
  6. 36.
    A stratified sample of 100 from a population of 1000 is split: 600 women and 400 men. After sampling, the survey finds 60 women say "yes" and 30 men. Estimate the overall population proportion of "yes" responses.
     
  7. 37.
    A class of 28 students completes a maths test. The teacher's class mean is 16/20 with range 7. The teacher reports "the school average is 16/20". Critique this claim.
     
  8. 38.
    A survey of 200 students yields a 95% confidence interval of "30–40% prefer pizza". Interpret this interval correctly. What does **not** it mean?
     
  9. 39.
    Design an unbiased question to estimate the proportion of students at your school who exercise daily, and state the sampling method.
     
  10. 40.
    A teacher cleans a dataset of 200 marks. She notices 15 zeros, 1 value of 100, and 5 missing entries. Outline a cleaning strategy.