Statistical inference — Question 2

QCAA 2022, Paper 1 · 1 mark

Q2 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 2

Which statement regarding sample means is true?

(A)

The distribution of

X

is always normally distributed.

(B)

The distribution of

\bar X

is always normally distributed.

(C)

The value of

\bar x

changes when different samples are selected.

(D)

The value of

\mu

changes when different samples are selected.

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer C

1 mark

ANSWER

Worked solution

\bar x

is a statistic calculated from a particular sample, so different random samples generally give different sample means. The population mean

\mu

is fixed, and neither

X

nor

\bar X

is always normally distributed without further conditions.

Selects option C.

[1 mark]

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

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