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

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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)

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