Sampling Practise A Level Unit 1

• Before redecorating the school canteen the headteacher decided to survey the opinion of staff and students.

  Explain why the headteacher decided to take a stratified sample of staff and students.​(1 mark)

  • to obtain a representative sample

  • large number of students compared to staff so would be unfair to take same numbers of both
• Before redecorating the school canteen the headteacher decided to survey the opinion of staff and students. Suggest a suitable sampling frame.​


  A list of the names of staff and students.
• Before redecorating the school canteen the headteacher decided to survey the opinion of staff and students.

  A member of staff or a student.
• Before redecorating the school canteen the headteacher decided to survey the opinion of staff

  Suggest a problem that might arise with the sampling frame when selecting the staff and students.​

  • absence on the day of the survey

  • sampling frame may contain errors
• As a pilot study the editor took a random sample of 25 subscribers.

  State two sources of uncertainty that could occur with sampling.​(2 marks)

  • Natural variation in a small sample

  • Bias
• ​A factory produces shopping bags for a large supermarket chain. The breaking load of a bag is the maximum load that it can carry before it breaks. The supermarket chain places an order for 50 000 shopping bags but wishes to know the breaking load of the bags.

  Suggest two reasons why a census would be unsuitable for this purpose.​(2 marks)

  • There are a very large number of bags

  • Bags are tested to destruction - there would be no bags left
• Jennifer is investigating the daily temperature at Perth. She wants to select a sample of size 5 from the daily temperatures at Perth from the first 20 days in May 1987.

  Describe what Jennifer could use as the sampling frame.​(1 mark)


  A list of the first two digits of the date.
• Jennifer is investigating the daily temperature at Perth. She wants to select a sample of size 5 from the daily temperatures at Perth from the first 20 days in May 1987.

  Describe the type of sample Jennifer could take and explain how she could collect her sample.​(2 marks)

  • Simple random sample

  • using a random number generator to select five dates.
• Sally is investigating rainfall in Leeming in 1987. The large data set provides data for 184 consecutive days in 1987.

  Describe how Sally could take a systematic sample of 30 days from the data for Leeming in 1987.​(3 marks)

  • Number ordered list of data.

  • Use random number generator is choose first selected piece of data.

  • Then take every 6th value
• Sally is investigating rainfall in Leeming in 1987. The large data set provides data for 184 consecutive days in 1987.

  Explain why Sally's sample would not necessarily give her 30 data points for her investigation.​(1 mark)


  Some data may be missing or erroneous
• ​A company claims that a quarter of the bolts sent to them are faulty. To test this claim the number of faulty bolts in a random sample of 50 is recorded.

  Give two reasons why a binomial distribution may be a suitable model for the number of faulty bolts in the sample. (2 marks)

  • Each bolt is either faulty or not faulty.

  • The probability of a bolt being faulty (or not) may be assumed constant.

  • Whether one bolt is faulty (or not) may be assumed to be independent (or does not affect the probability of) whether another bolt is faulty (or not).

  • There is a fixed number of bolts (50)
• Define the critical region of a test statistic.​ (2 marks)

  The set of values of the test statistic for which the null hypothesis is rejected in a hypothesis test
• ​Explain why even if the population product moment correlation coefficient between two variables is close to zero there may still be a relationship between them.​(2 marks)

  • correlation shows there is NO (OR EXTREMELY WEAK) LINEAR RELATIONSHIP between the two variables.

  • For example, there could be a NON-LINEAR RELATIONSHIP between the two variables.
• What is the definition of a critical value?​(1 mark)

  A critical value is the point (or points) on the scale of the test statistic beyond which we reject the null hypothesis
• State the definition of a hypothesis test.​(1 mark) PMCC

  A hypothesis test is a statistical test that is used to determine whether there is enough evidence in a SAMPLE OF DATA to infer that a certain condition is true for the ENTIRE POPULATION
• State the definition of a test statistic.​(1 mark)

  A statistic that is calculated from sample data in order to test a hypothesis about a population
• ​State what is measured by the product moment correlation coefficient.​(1 mark)

  Linear association between two variables.
• State the conditions under which the normal distribution may be used as an appoximation to the binomial distribution X ~ B(n, p).​(2 marks)


  • n is large

  • p is close to 0.5
• A manufacturer claims that more than 55% of its batteries last for at least 15 hours of continuous use. Write down a reason why the manufacturer should not justify their claim by testing all the batteries they produce.​(1 mark)

  There would be no batteries left.
• A manufacturer claims that more than 55% of its batteries last for at least 15 hours of continuous use.

  To test the manufacturer's claim, a random sample of 300 batteries were tested.

  State the hypotheses for a one-tailed test of the manufacturer's claim.​(1 mark)

  H0: p = 0.55 H1: p > 0.55
• In an experiment a group of children each repeatedly throw a dart at a target. For each child, the random variable H represents the number of times the dart hits the target in the first 10 throws.

  Peta models H as B(10, 0.1)

  State two assumptions PETA needs to make to use her model. (2 marks)

  • the probability of a dart hitting the target is constant (from child to child and for each throw by each child)

  • the throws of each of the darts are independent
• Charlie is studying the time it takes members of his company to travel to the office.

  He stands by the door to the office from 08 40 to 08 50 one morning and asks workers, as they arrive, how long their journey was.

  State the sampling method Charlie used. (1 mark)

  Convenience or opportunity (sampling)
• Charlie is studying the time it takes members of his company to travel to the office.

  He uses a opportunity sampling method.

  State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers. (2 marks)

  • quota (sampling)

  • e.g. take 4 people every 10 minutes
• Taruni decided to ask every member of the company the time, x minutes, it takes them to travel to the office.

  State the selection process Taruni used. (1 mark)

  Census
• Sara is investigating the variation on daily maximum gust, t kn, for Camborne in June and July 1987.

  She used the large data set to select a sample of size 20 from the June and July data for 1987. Sara selected the first value using a random number from 1 to 4 and then selected every third value after that.

  From your knowledge of the large data set explain why this process may not generate a sample of size 20. (1 mark)

  In LDS some days have gaps because the data was not recorded
• Give a reason why Sara might include an outlier. (1 mark)

  It is a piece of data and we should consider all the data
• Give a reason why Sara might exclude an outlier. (1 mark)

  It is an extreme value and could unduly influence the analysis/it could be a mistake
• John decided to use the regression line to estimate the daily rainfall for a day in December when the daily mean pressure is 1011 hPa. Using your knowledge of the large data set, comment on the reliability of John's estimate. (1 mark)

  Unreliable, as the large data set does not cover December
• Using your knowledge of the large data set, suggest, giving a reason, which month in Camborne in 1987 had the highest daily mean wind speed. (2 marks)

  • October since

  • it is windier in the autumn/month of the hurricane/latest month in the year
• Using your knowledge of the large data set, suggest the names of the two places in the Northern hemisphere with the highest mean temperatures for the month of July in 2015. (1 mark)

  Beijing and Jacksonville
• Using your knowledge of the large data set, and with reference to the locations, give a reason why Beijing and Jacksonville have the highest temperatures in July. (1 mark)


  Beijing and Jacksonville are the closest to the equator
• When can you display data in a histogram?

  Continuous data with unequal class widths