Zadanie 7c, Paper 1, listopad 2023, TZ2, Matematyka AA IB SL
Wzorowane na: Matematyka AA IB SL — listopad 2023, TZ2, Paper 1 (zadania wzorowane), pytanie 7(c). Treść, dane i kontekst są zmienione; sprawdzane umiejętności, format i punktacja jak w oryginale.
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Zadanie
Wspólne informacje do wiązki zadań
A laboratory processed 20000 specimens over 50 working days. Its daily capacity was 600 specimens. The daily counts n are grouped below. For a handling audit, staff will inspect 10% of arriving specimens. Specimens are either refrigerated or ambient-temperature; the proportions in these categories are known.
| Daily count n | Days |
|---|---|
| 0<n≤150 | 4 |
| 150<n≤300 | p |
| 300<n≤450 | 14 |
| 450<n≤600 | 20 |
Polecenie
(i) Give one disadvantage of inspecting only the first 10% of arrivals. (ii) Describe systematic sampling of 10% of arrivals. (iii) Name a method that sets sample numbers to match the known proportions of refrigerated and ambient specimens.
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Odpowiedź z klucza
(i) The earliest arrivals may come from the same dispatch batch or supplier, so time-dependent handling conditions are underrepresented. (ii) Choose a random starting arrival among the first 10, then inspect every tenth arrival. (iii) Quota sampling with category quotas proportional to the known population proportions; proportional stratified sampling with random selection inside categories also achieves this objective.
Schemat punktowania
(i) A1:a concrete reason for selection bias, beyond merely saying the sample is unrepresentative. (ii) A1:regular intervals. A1:interval 10. A random start is good practice but its omission alone does not lose these two marks. (iii) A1:quota sampling; accept proportional stratified sampling when the allocation/selection is described correctly.
Komentarz. Paper 1: no calculator; AA SL formula booklet allowed. Give exact results unless a graph estimate is requested.