Statistical inference — Question 10

QCAA 2021, Paper 1 · 1 mark

Q10 · 2021 · Technology-freeSimple familiar1 mark

QUESTION 10

The 2016 Australian census recorded the number of bedrooms per household. The results are summarised in the histogram, as shown. Based on this data, the mean number of bedrooms per household was calculated to be

3.5

Fifty samples of size

40

were randomly selected from the census data and the sample means recorded.

The histogram that most likely represents the distribution of the sample means is

Original household histogram and four candidate sampling-distribution histograms.

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

Worked solution

The sampling distribution of

\bar X

should be centred near the population mean

3.5

and, for samples of size

40

, should be more nearly normal and much less spread out than the original household distribution. Option D has those features.

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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