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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. Arandom 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- Let it; = the population mean breaking strength of the ith type of cloth, i = 1, 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 of ii. ,i = 1, 2. 3, 4. [2] (e) Work out SST, SS: and 55 E . Hence, construct an ANOVA table. Show all the necessary steps in getting the answers. [9] (1) Perform the hypothesis testing suggested in part (b). State the following clearly: (i) Critical value at the 5% level ofsignicance [1] (ii) Rejection region [1] (iii) Decision with reason [2] (iv) Conclusion [1]