题目
The Headteacher of a school is thinking about making changes to the school day.
She wants to take a sample of 60 students so that she can find out what the students think about the proposed changes.
The names of the 1200 students of the school are listed alphabetically.
(a) Explain how the Headteacher could take a systematic sample of 60 students.
(b) (i) Explain why systematic sampling is likely to be quicker than simple random sampling in this situation.
(ii) With reference to this situation,
• explain why systematic sampling may introduce bias compared to simple random sampling • give an example of the bias that may occur when using this alphabetical list
When the Headteacher completes the systematic sample of size 60 she finds that 6 students were to be selected from Year 9.
The Head of Mathematics suggests that a stratified sample of size 60 would be a more appropriate method.
There were 200 students in Year 9.
(c) Explain why this suggests that a stratified sample of size 60 may be better than the systematic sample taken by the Headteacher.
题目中文翻译
一所学校的校长正在考虑对上课日做出一些改变。
她希望抽取 60 名学生的样本，以了解学生对拟议改动的看法。
该校 1200 名学生的名字按字母顺序排列。
(a) 说明校长如何抽取 60 名学生的系统抽样。
(b) (i) 说明为什么在这种情况下，系统抽样可能比简单随机抽样更快。
(ii) 针对这个情境，
• 说明为什么与简单随机抽样相比，系统抽样可能引入偏差 • 给出使用这份按字母顺序排列的名单时可能出现的偏差示例
当校长完成 60 人的系统抽样后，她发现其中 6 名学生应来自 9 年级。
数学科主任建议，抽取 60 人的分层抽样可能更合适。
9 年级共有 200 名学生。
(c) 说明为什么这表明 60 人的分层抽样可能比校长所做的系统抽样更好。