Statistical inference — Question 8

QCAA 2024, Paper 2 · 1 mark

Q8 · 2024 · Technology-activeSimple familiar1 mark

QUESTION 8

T

is a random variable. A random sample of four values of

T

is collected and used to produce an approximate confidence interval for the population mean of

(3.3,4.1)

. Given that three of the sample values are 3.4, 3.6 and 3.9, the remaining sample value is

(A)

3.6

(B)

3.7

(C)

3.8

(D)

3.9

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

Worked solution

The confidence interval is centred on the sample mean, so

\bar t=(3.3+4.1)/2=3.7

. The four observations therefore sum to

14.8

. The known three sum to

10.9

, leaving

14.8-10.9=3.9

Selects option D.

[1 mark]

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

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