University statistical inference test to download as PDF

This University statistical inference test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 18-19, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – A confidence interval
A sample of 50 commuting times has \(\bar x=31.2\) minutes and \(s=4.5\) minutes.
1. Find a 95% confidence interval for the mean commuting time. (3 marks)
2. Explain what "95% confidence" means. (1 mark)
Question 2 – A z-test
Exam marks have \(\sigma=10\). A school claims its mean is 75. A sample of 40 students has mean \(78.5\). Test \(H_0:\mu=75\) against \(H_1:\mu\ne75\) at 5%.
Question 3 – A t-test
A normal sample of 9 values has \(\bar x=10.8\) and \(s=1.2\). Test \(H_0:\mu=10\) against \(H_1:\mu>10\) at 5%.
Question 4 – A test of independence
The table shows whether 120 students passed a test, by whether they attended a revision session.
Passed Failed
Attended 40 20
Did not attend 30 30
1. Find the expected frequencies. (1 mark)
2. Calculate \(\chi^2\) (without continuity correction) and test at 5%. (3 marks)
Question 5 – Problem: regression
For 8 pairs, \(\sum x=40\), \(\sum y=96\), \(S_{xx}=42\) and \(S_{xy}=63\).
1. Find the regression line of \(y\) on \(x\). (2 marks)
2. Predict \(y\) at \(x=6\) and comment on a prediction at \(x=20\) when the \(x\) values lie between 1 and 9. (2 marks)

	Passed	Failed
Attended	40	20
Did not attend	30	30

How to use this University statistical inference test

First, revise with the statistical inference lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the statistical inference test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this University statistical inference test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.