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A-Level MathematicsYear 2022Q2

6   2. A factory produces yellow tennis balls and white tennis balls. Independent samples, one of yellow tennis balls and one of white tennis balls, are taken. The table shows information about the weights of the yellow tennis balls, Y grams, and the weights of the white tennis balls, W grams. Sample size Mean weight of random sample (grams) Known population standard deviation of weights (grams) Yellow tennis balls 120 57.2 1.2 White tennis balls 140 56.9 0.9 (a) Find a 95% confidence interval for the mean weight of yellow tennis balls. (3) Jamie claims that the mean weight of the population of yellow tennis balls is greater than the mean weight of the population of white tennis balls. A test of Jamie’s claim is carried out. (b) (i) Specify the approximate distribution of Y– – W– under the null hypothesis of the test. (3) (ii) Explain the relevance of the large sample sizes to your answer to part (i). (1) (c) Complete the hypothesis test using a 5% level of significance. You should state your hypotheses and the value of your test statistic clearly. (5) ___________________________________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 7   Question 2 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___________________________________________

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)