A-Level MathematicsYear 2022Q5
14 5. The concentration of an air pollutant is measured in micrograms/m3 Samples of air were taken at two different sites and the concentration of this particular air pollutant was recorded. For Site A the summary statistics are shown below. number of samples s 2 A Site A 13 6.39 For Site B there were 9 samples of air taken. A test of the hypothesis H0 : σ 2 A = σ 2 B against the hypothesis H1 : σ 2 A ≠ σ 2 B is carried out using a 2% level of significance. (a) State a necessary assumption required to carry out the test. (1) Given that the assumption in part (a) holds, (b) find the set of values of s 2 B that would lead to the null hypothesis being rejected, (4) (c) find a 99% confidence interval for the variance of the concentration of the air pollutant at Site A. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 15 Question 5 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 5 is 8 marks)
Paper Source:9fm0-4b-que-20220628.pdf
Get full Socratic AI guidance on this question — free in the Applaa desktop app
Appy Buddy guides you step-by-step toward the answer without giving it away. Type your attempt and get instant, mark-scheme-aware clues that teach you to think like an examiner.
Applaa Desktop App
Join Applaa Community
Create your own games, learn AI concepts, program interactive apps, and share with a kid-safe community approved by parents. Free forever on Windows and Mac.
Download Free
Available for Windows and macOS · COPPA Compliant
Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
Syllabus levelAdvanced Level (A-Level)
SubjectMathematics
Official MarksVariable (2–6 marks)