Tom wants a sample of Year 7 students and a sample of Year 11 students to complete a questionnaire for him. He considers these three sampling methods for Year 7 students.

Method A
Number all the students in Year 7. Obtain 30 random numbers. Ask the students whose random numbers come up to complete the questionnaire.

Method B
Wait outside the dinner hall. Ask the first 30 Year 7 students he sees to complete the questionnaire.

Method C
Choose three Year 7 students from each of the 10 maths sets. Ask these students to complete his questionnaire.

Name and compare the merits of each sampling method. Make a reasoned choice of which method Tom should use.

This question requires an evaluation of three different sampling methods. * **Method A is Simple Random Sampling.** Its main advantage is that it is free from bias, as every student has an equal chance of being selected. This makes it likely to be representative. A disadvantage is the practical effort of numbering everyone and generating random numbers. * **Method B is Convenience Sampling.** Its only advantage is that it is quick and easy. However, it is a non-random method and is highly susceptible to bias. The sample is unlikely to be representative of the entire year group. * **Method C is Stratified Sampling.** The population is divided into strata (maths sets). The advantage is that it guarantees representation from all strata (in this case, all ability levels). A potential disadvantage is that it is not a proportional sample; it takes 3 students from each set regardless of the set's size. If Set 1 has 30 students and Set 10 has 15, this method would over-represent Set 10. **Conclusion:** Method B is the worst choice due to the high risk of bias. Between A and C, Method A is a very strong choice as it is purely random and unbiased. Method C is also strong but has a potential flaw if the set sizes are unequal. A good conclusion would be to recommend Method A as the most reliable way to get an unbiased sample without making assumptions about the sizes of the maths sets.