- A tennis club's committee wishes to select a sample of 50 members to fill in a questionnaire about the club's facilities. The 300 members, of whom 180 are males, are listed in alphabetical order and numbered \(1 - 300\) in the club’s membership book.
The club's committee decides to use a random number table to obtain its sample.
The first three lines of the random number table used are given below.
| 319 | 952 | 241 | 343 | 278 | 811 | 394 | 165 | 008 | 413 | 063 | 179 | 749 |
| 722 | 962 | 334 | 461 | 267 | 114 | 806 | 992 | 414 | 837 | 837 | 657 | 339 |
| 470 | 684 | 554 | 127 | 067 | 459 | 142 | 920 | 144 | 575 | 311 | 605 | 412 |
Starting with the top left-hand corner (319) and working across, the committee selects 50 random numbers. The first 2 suitable numbers are 241 and 278. Numbers greater than 300 are ignored.
- Find the next two suitable numbers.
When the club's committee looks at the members corresponding to their random numbers they find that only 1 female has been selected.
The committee does not want to be accused of being biased towards males so considers using a systematic sample instead. - Explain clearly how the committee could take a systematic sample.
- Explain why a systematic sample may not give a sample that represents the proportion of males and females in the club.
The committee decides to use a stratified sample instead.
- Describe how to choose members for the stratified sample.
- Explain an advantage of using a stratified sample rather than a quota sample.