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Question 2 (20 marks) A manufacturer produces fashions that require different types of cloth. Four types of cloth are considered. He wants to know if there is any difference among the mean breaking strength (in Newton) of the four types of cloth. A random sample of 24 pieces of cloth of the same size, six of each type, are used to record the breaking strength. The table below shows the breaking strength data: Observation (yi -) Mean Breaking Strength (17;. l 41 35 48 40 45 52 ' . 2 32 37 46 53 41 3 35 30 24 26 28 4 33 27 36 35 27 Let u; = the population mean breaking strength of the i-th type of cloth, 1' = I, 2, 3, 4. (a) What distributional assumption is required for the breaking strength data above? [1] (b) Suggest a suitable hypothesis testing method to test the differences among the population mean breaking strength data for the 4 types of cloth. [1] (c) State the null and alternative hypotheses, H0 and H1. [2] (d) Compute the values offli. ,t' = 123,4. [2]