2.01a Population and sample: terminology

105 questions

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Edexcel S2 Q1
7 marks Easy -1.8
Explain what you understand by
  1. a population, [1]
  2. a statistic. [2]
A questionnaire concerning attitudes to classes in a college was completed by a random sample of 50 students. The students gave the college a mean approval rating of 75\%.
  1. Identify the population and the statistic in this situation. [2]
  2. Explain what you understand by the sampling distribution of this statistic. [2]
Edexcel S2 Q1
4 marks Easy -2.0
The manager of a leisure club is considering a change to the club rules. The club has a large membership and the manager wants to take the views of the members into consideration before deciding whether or not to make the change.
  1. Explain briefly why the manager might prefer to use a sample survey rather than a census to obtain the views. [2]
  2. Suggest a suitable sampling frame. [1]
  3. Identify the sampling units. [1]
Edexcel S2 Q6
20 marks Moderate -0.3
A magazine has a large number of subscribers who each pay a membership fee that is due on January 1st each year. Not all subscribers pay their fee by the due date. Based on correspondence from the subscribers, the editor of the magazine believes that 40\% of subscribers wish to change the name of the magazine. Before making this change the editor decides to carry out a sample survey to obtain the opinions of the subscribers. He uses only those members who have paid their fee on time.
  1. Define the population associated with the magazine. [1]
  2. Suggest a suitable sampling frame for the survey. [1]
  3. Identify the sampling units. [1]
  4. Give one advantage and one disadvantage that would have resulted from the editor using a census rather than a sample survey. [2]
As a pilot study the editor took a random sample of 25 subscribers.
  1. Assuming that the editor's belief is correct, find the probability that exactly 10 of these subscribers agreed with changing the name. [3]
In fact only 6 subscribers agreed to the name being changed.
  1. Stating your hypotheses clearly test, at the 5\% level of significance, whether or not the percentage agreeing to the change is less that the editor believes. [5]
The full survey is to be carried out using 200 randomly chosen subscribers.
  1. Again assuming the editor's belief to be correct and using a suitable approximation, find the probability that in this sample there will be least 71 but fewer than 83 subscribers who agree to the name being changed. [7]
Edexcel S2 Q1
4 marks Easy -1.2
Explain briefly what you understand by
  1. a statistic, [2]
  2. a sampling distribution. [2]
Edexcel S2 Q1
5 marks Easy -2.0
A large dental practice wishes to investigate the level of satisfaction of its patients.
  1. Suggest a suitable sampling frame for the investigation. [1]
  2. Identify the sampling units. [1]
  3. State one advantage and one disadvantage of using a sample survey rather than a census. [2]
  4. Suggest a problem that might arise with the sampling frame when selecting patients. [1]
Edexcel S2 2004 January Q1
5 marks Easy -1.8
A large dental practice wishes to investigate the level of satisfaction of its patients.
  1. Suggest a suitable sampling frame for the investigation. [1]
  2. Identify the sampling units. [1]
  3. State one advantage and one disadvantage of using a sample survey rather than a census. [2]
  4. Suggest a problem that might arise with the sampling frame when selecting patients. [1]
Edexcel S2 2002 June Q2
5 marks Easy -1.2
A random sample \(X_1, X_2, \ldots, X_n\) is taken from a finite population. A statistic \(Y\) is based on this sample.
  1. Explain what you understand by the statistic \(Y\). [2]
  2. Give an example of a statistic. [1]
  3. Explain what you understand by the sampling distribution of \(Y\). [2]
Edexcel S2 2004 June Q1
3 marks Easy -1.8
Explain briefly what you understand by
  1. a sampling frame, [1]
  2. a statistic. [2]
Edexcel S2 2006 June Q1
3 marks Easy -2.0
Before introducing a new rule the secretary of a golf club decided to find out how members might react to this rule.
  1. Explain why the secretary decided to take a random sample of club members rather than ask all the members. [1]
  2. Suggest a suitable sampling frame. [1]
  3. Identify the sampling units. [1]
Edexcel S2 2010 June Q1
5 marks Easy -1.8
Explain what you understand by
  1. a population, [1]
  2. a statistic. [1]
A researcher took a sample of 100 voters from a certain town and asked them who they would vote for in an election. The proportion who said they would vote for Dr Smith was 35\%.
  1. State the population and the statistic in this case. [2]
  2. Explain what you understand by the sampling distribution of this statistic. [1]
Edexcel S2 Specimen Q1
4 marks Easy -1.8
A school held a disco for years 9, 10 and 11 which was attended by 500 pupils. The pupils were registered as they entered the disco. The disco organisers were keen to assess the success of the event. They designed a questionnaire to obtain information from those who attended.
  1. State one advantage and one disadvantage of using a sample survey rather than a census. [2]
  2. Suggest a suitable sampling frame. [1]
  3. Identify the sampling units. [1]
Edexcel S2 Q1
4 marks Easy -2.0
  1. Explain why it is often useful to take samples as a means of obtaining information. [2 marks]
  2. Briefly define the term sampling frame. [1 mark]
  3. Suggest a suitable sampling frame for a sample survey on a proposal to install speed humps on a road. [1 mark]
Edexcel S2 Q1
3 marks Easy -1.8
  1. Explain briefly why it is often useful to take a sample from a population. [2 marks]
  2. Suggest a suitable sampling frame for a local council to use to survey attitudes towards a proposed new shopping centre. [1 mark]
Edexcel S2 Q1
4 marks Easy -1.8
An insurance company is investigating how often its customers crash their cars.
  1. Suggest an appropriate sampling frame. [1 mark]
  2. Describe the sampling units. [1 mark]
  3. State the advantage of a sample survey over a census in this case. [2 marks]
Edexcel S2 Q1
3 marks Easy -1.8
A company that makes ropes for mountaineering wants to assess the breaking strain of its ropes.
  1. Explain why a sample survey, and not a census, should be used. [2 marks]
  2. Suggest an appropriate sampling frame. [1 mark]
Edexcel S2 Q2
6 marks Easy -2.0
  1. Give one advantage and one disadvantage of
    1. a sample survey, [2 marks]
    2. a census. [2 marks]
  2. Suggest a situation in which each could be used. [2 marks]
Edexcel S2 Q1
4 marks Easy -1.8
Briefly explain what is meant by
  1. a statistical model, [2 marks]
  2. a sampling frame, [1 mark]
  3. a sampling unit. [1 mark]
Edexcel S2 Q4
10 marks Moderate -0.8
A teacher wants to investigate the sports played by students at her school in their free time. She decides to ask a random sample of 120 pupils to complete a short questionnaire.
  1. Give two reasons why the teacher might choose to use a sample survey rather than a census. [2 marks]
  2. Suggest a suitable sampling frame that she could use. [1 mark]
The teacher believes that 1 in 20 of the students play tennis in their free time. She uses the data collected from her sample to test if the proportion is different from this.
  1. Using a suitable approximation and stating the hypotheses that she should use, find the critical region for this test. The probability for each tail of the region should be as close as possible to 5\%. [6 marks]
  2. State the significance level of this test. [1 mark]
Edexcel S2 Q1
5 marks Easy -1.8
  1. Explain what you understand by the term sampling frame when conducting a sample survey. [1 mark]
  2. Suggest a suitable sampling frame and identify the sampling units when using a sample survey to study
    1. the frequency with which cars break down in the first 3 months after being serviced at a particular garage,
    2. the weight loss of people involved in trials of a new dieting programme.
    [4 marks]
Edexcel S2 Q1
6 marks Easy -1.8
  1. Explain briefly what you understand by the terms
    1. population,
    2. sample.
    [2 marks]
  2. Giving a reason for each of your answers, state whether you would use a census or a sample survey to investigate
    1. the dietary requirements of people attending a 4-day residential course,
    2. the lifetime of a particular type of battery.
    [4 marks]
Edexcel S2 Q1
4 marks Easy -2.0
  1. State one advantage and one disadvantage in using a census rather than a sample survey in statistical work. [2]
  2. Give an example of a situation in which you would choose to use a census rather than a sample survey and explain why. [2]
OCR MEI S3 2008 June Q1
19 marks Moderate -0.8
  1. Sarah travels home from work each evening by bus; there is a bus every 20 minutes. The time at which Sarah arrives at the bus stop varies randomly in such a way that the probability density function of \(X\), the length of time in minutes she has to wait for the next bus, is given by $$f(x) = k(20-x) \text{ for } 0 \leq x \leq 20, \text{ where } k \text{ is a constant.}$$
    1. Find \(k\). Sketch the graph of \(f(x)\) and use its shape to explain what can be deduced about how long Sarah has to wait. [5]
    2. Find the cumulative distribution function of \(X\) and hence, or otherwise, find the probability that Sarah has to wait more than 10 minutes for the bus. [4]
    3. Find the median length of time that Sarah has to wait. [3]
    1. Define the term 'simple random sample'. [2]
    2. Explain briefly how to carry out cluster sampling. [3]
    3. A researcher wishes to investigate the attitudes of secondary school pupils to pollution. Explain why he might prefer to collect his data using a cluster sample rather than a simple random sample. [2]
AQA AS Paper 2 2023 June Q12
1 marks Easy -2.5
The mass of a bag of nuts produced by a company is known to have a mean of 40 grams and a standard deviation of 3 grams. The company produces five different flavours of nuts. The bags of nuts are packed in large boxes. Given the information above, identify the continuous variable from the options below. Tick (\(\checkmark\)) one box. [1 mark] The flavours of the bags of nuts The known standard deviation of the mass of a bag of nuts The mass of an individual bag of nuts The number of bags of nuts in a large box
AQA Paper 3 2018 June Q13
3 marks Easy -1.8
The table below shows an extract from the Large Data Set.
Year2011201220132014\% change since 2011
Other takeaway food brought home0000\(-29\)
Sarah claims that the \(-29\%\) change since 2011 is incorrect, as there is no change between 2011 and 2014. Using your knowledge of the Large Data Set to justify your answer, explain whether Sarah's claim is correct. [3 marks]
AQA Paper 3 2022 June Q15
3 marks Easy -1.8
Researchers are investigating the average time spent on social media by adults on the electoral register of a town. They select every 100th adult from the electoral register for their investigation.
  1. Identify the population in their investigation. [1 mark]
    1. State the name of this method of sampling. [1 mark]
    2. Describe one advantage of this sampling method. [1 mark]