population and sample proportion
Practise population and sample proportion with an original VectorPaths question, worked explanation and related VCE Methods practice.
4 practice marks
Original practice question
A school has 1,200 Year 12 students. A simple random sample of 80 of these students is selected, and 28 students in the sample say they cycle to school. (a) Identify the population and the sample. (2 marks) (b) Calculate the sample proportion who cycle to school. (1 mark) (c) Explain why this sample proportion is not necessarily the population proportion. (1 mark)
Worked explanation
- Identify the population
The population is all 1,200 Year 12 students at the school: the complete group the study concerns.
- Identify the sample
The sample is the 80 selected Year 12 students. The 28 cyclists are a subset of the sample, not the whole sample.
- Calculate the sample proportion
\[\hat p=\frac{28}{80}=0.35=35\%.\]
- Distinguish an estimate from the population value
The population proportion p concerns all 1,200 students and is not given. The sample proportion is calculated from only 80 students and varies between samples, so 0.35 is an estimate of p, not an exact known population value.
Population: all 1,200 Year 12 students. Sample: the 80 selected students. Sample proportion: 0.35. The population proportion is unknown; sampling variation means the two need not be equal.
Original VectorPaths practice; not an official VCAA question or marking rubric.