Before discussing normality or sample size, identify the population and how observations were selected. A large collection of convenient observations may still give biased information about the target population.
| Condition | What to check |
|---|---|
| Random selection | The selection mechanism should not systematically favour a particular part of the population. |
| Common population | Observations should concern the same population and comparable conditions for the proposed model. |
| Independence | One observation should not systematically determine another. Repeated measurements on the same person may be dependent. |
Bridge the idea
A school wants the mean journey time of all its students. It surveys 500 students who arrive before 7 a.m. Is the large sample enough? No: later arrivals are excluded, so the sampling method may systematically misrepresent the target population. Increasing the same biased sample does not fix the selection problem.
A random sample and independent observations address different issues. Sampling without replacement from a finite population is not exactly independent; independence may be a reasonable approximation when the sample is a small proportion of that population.
Exam wording: “Assume the observations form an independent random sample from the stated population.” If a flaw is evident, name it in context: “Students arriving later are excluded, so the sample may be biased.” Normality is a separate distribution question.
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