Statistical inference — Question 10

QCAA 2023, Paper 1 · 1 mark

Q10 · 2023 · Technology-freeSimple familiar1 mark

QUESTION 10

A random variable is drawn from a population with the distribution shown in the histogram. A number of samples of size 10 were randomly selected from this distribution and the sample means,

\bar x

, were recorded. The histogram that most likely represents the distribution of the sample means is

Histogram of the population distribution used in Question 10.

Four candidate histograms A to D for the distribution of the sample means.

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

Worked solution

The sampling distribution of

\bar X

has the same mean as the population but a smaller spread. For samples of size 10 it is also more concentrated and closer to a bell-shaped distribution. Option B has the appropriate centre and substantially reduced spread.

Selects option B.

[1 mark]

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

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