Statistical inference — Question 10

QCAA 2021, Paper 2 · 1 mark

Q10 · 2021 · Technology-activeSimple familiar1 mark

QUESTION 10

A random variable is normally distributed with a mean,

\mu

. An approximate

95\%

confidence interval for

\mu

from a sample from this distribution is

(209.7,221.9)

An approximate confidence interval for

\mu

based on the same sample, using a confidence level greater than

95\%

, could be

(A)

(206.5,222.3)

(B)

(208.5,223.1)

(C)

(210.6,221.0)

(D)

(215.8,228.0)

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

Worked solution

The original interval has centre

(209.7+221.9)/2=215.8

. For the same sample, a higher confidence level must keep the same centre but have a larger width. Option B is centred at

215.8

and is wider than the

95\%

interval.

Selects option B.

[1 mark]

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

View the full QCAA marking guide

Related questions

Q4 · 2025 QCAA · Paper 1 · 1 mark
$X$ is a random variable with mean $\mu$ and standard deviation $\sigma$ . From random samples of $X$ values, each of size $n$ , the sample mean is calculated. This sampling and calculation is repeated a large number of times. The mean of the distribution of the sample means would be approximately
Statistical inference
Q9 · 2025 QCAA · Paper 1 · 1 mark
An approximate confidence interval for a population mean is calculated based on a sample size of 16 and is found to have width, $w$ . A second confidence interval is calculated from another sample with the same sample standard deviation. Given that the same $z$ -value was used for both intervals and the width of the second interval is $2w$ , what is the size of…
Statistical inference
Q14 · 2025 QCAA · Paper 1 · 5 marks
A factory produces cans of juice. Each can has a labelled volume of 500 mL.
The factory manager conducted a random sample of 100 cans to assess whether the labelled volume was being met satisfactorily in production. The mean volume of the sample was 498.9 mL with a sample standard deviation of 4.0 mL.
Statistical inference
Q5 · 2025 QCAA · Paper 2 · 1 mark
The height (cm) of people in a certain population is normally distributed with a standard deviation of $7.42$ cm.
A researcher takes repeated random samples of $15$ people and calculates the mean height for each sample.
The expected standard deviation (cm) of the distribution of these sample mean heights would be approximately
Statistical inference