Statistical inference — Question 5

QCAA 2022, Paper 1 · 1 mark

Q5 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 5

Four random samples of different sizes were taken to estimate a certain population mean, given a known population standard deviation. A

95\%

confidence interval was calculated for each sample.

Which sample used the largest sample size?

(A)

Sample 1

(B)

Sample 2

(C)

Sample 3

(D)

Sample 4

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

Worked solution

With the same confidence level and population standard deviation, confidence-interval width is proportional to

1/\sqrt n

. The narrowest interval therefore corresponds to the largest sample size. Sample 1 has the narrowest interval.

Selects option A.

[1 mark]

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

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