Statistical inference — Question 10

QCAA 2020, Paper 2 · 1 mark

Q10 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 10

The time taken by the Year 7 students at a particular school to complete a standardised test is known to be normally distributed. A researcher claims that the population mean is

8.2

minutes.

The mean time taken to complete this test by a sample of

10

of these students is

8.1

minutes with a standard deviation of

1.2

minutes.

The

95\%

confidence interval for

\mu

based on this sample is

(A)

(7.36,8.84)

minutes

(B)

(7.46,8.94)

minutes

(C)

(7.86,8.33)

minutes

(D)

(7.96,8.44)

minutes

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

Worked solution

Using the syllabus normal approximation,

\bar x\pm1.96\,s/\sqrt n=8.1\pm1.96(1.2/\sqrt{10})\approx8.1\pm0.744

, giving approximately

(7.36,8.84)

minutes.

Selects option A.

[1 mark]

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

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