Practise this objective
AI-marked practice questions tied to QCAA mark schemes for this exact LO. Free to start.
Start free practicePractice questions for this objective
Full questions, answers and worked solutions unlock when you start a free practice session.
Question 1
A national health survey estimates the mean daily water intake of adults in a region. A random sample of \(250\) adults yielded a sample mean of \(2.15\) litres with a sample standard deviation of \(0.40\) litres.
(a) Determine the \(90\%\) confidence interval for the population mean daily water intake. (2 marks)
(b) A nutritionist claims that the population mean daily water intake is at least \(2.30\) litres. Evaluate whether this claim is supported by the \(90\%\) confidence interval. (2 marks)
(c) Explain what the \(90\%\) confidence level means in the context of this survey. (1 mark)
Worked answer
🔒 Start free to see full answer
Question 2
A researcher measures the heights of 80 randomly selected students from a large school population and calculates a 95% confidence interval for the mean height. Which statement best describes what the 95% confidence interval represents?
Worked answer
🔒 Start free to see full answer
Question 3
A manufacturer of precision springs tests a random sample of \(80\) springs to estimate the mean breaking load. The sample yields a mean breaking load of \(52.3\) kg with a standard deviation of \(3.6\) kg.
The manufacturer claims that a \(95\%\) confidence interval for the mean breaking load of all springs produced is \((51.5, 53.1)\) kg.
Determine whether the manufacturer's confidence interval is correct.
Worked answer
🔒 Start free to see full answer
Question 4
A community health researcher surveyed a random sample of 64 adults about their daily water intake. The sample mean was found to be \(2.4\) litres with a standard deviation of \(0.8\) litres.
Determine the approximate 95% confidence interval for the mean daily water intake of adults in the community, using \(z = 2\). Express your answer in litres, correct to two decimal places.
Worked answer
🔒 Start free to see full answer
Question 5
A wildlife researcher measures the wingspan of a sample of 150 birds from a large forest population and constructs a 95% confidence interval for the population mean wingspan. The interval is $(24.8 \text{ cm}, 26.2 \text{ cm})$. Which statement correctly interprets this interval estimate?
Worked answer
🔒 Start free to see full answer
More in Confidence intervals for proportions