4. 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.
- Give two reasons why the teacher might choose to use a sample survey rather than a census.
- Suggest a suitable sampling frame that she could use.
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.
- 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\%.
- State the significance level of this test.