QCEVault

Statistical inference — Question 13

QCAA 2022, Paper 2 · 5 marks

Q13 · 2022 · Technology-activeSimple familiar5 marks

QUESTION 13 (5 marks)

An article claims that the mean starting salary of graduates in Australia is currently $64 800\char36 64\,800 with a standard deviation of $4500\char36 4500.
To check the validity of this claim, an employment agent intends to collect data on the starting salaries of a random sample of 360 graduates.
a)
Determine the probability that the sample mean starting salary will be between $64 000\char36 64\,000 and $65 000\char36 65\,000.
[2 marks]
b)
From the data, the agent calculates a confidence interval for the population mean starting salary of ($64 589\char36 64\,589, $65 811\char36 65\,811). Determine the sample mean.
[1 mark]
c)
Comment on the reasonableness of the article’s claim based on this confidence interval.
[2 marks]
Question linkOriginal paper

Related questions

  1. Q4 · 2025 QCAA · Paper 1 · 1 mark
    XX is a random variable with mean μ\mu and standard deviation σ\sigma. From random samples of XX values, each of size nn, 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
  2. 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, ww. A second confidence interval is calculated from another sample with the same sample standard deviation. Given that the same zz-value was used for both intervals and the width of the second interval is 2w2w, what is the size of…
    Statistical inference
  3. 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
  4. Q5 · 2025 QCAA · Paper 2 · 1 mark
    The height (cm) of people in a certain population is normally distributed with a standard deviation of 7.427.42 cm.
    A researcher takes repeated random samples of 1515 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