A study was undertaken to examine the tensile strength of a new type of polyester fibre. Where random sample of n = 30 observations. The existing type of polyester fibre that the new type is designed to replace has a mean breaking strength of 0.26 grams/denier. The study wants to test whether the mean breaking strength of the new type of polyester fibre differs from the mean breaking strength of the existing type of polyeste fibre. (i) Write down appropriate null and alternative hypotheses for a test of whether the mean breaking strength of the new type of polyester fibre differs from the mean breaking strength of the existing type of polyester fibre. Define any notation that you use. (ii) It is proposed to use a z-test to test the hypotheses specified in part (a)(i). Justify this choice of test in terms of the sample size, n. (iii) Write down the formula for the test statistic used in the z-test of part (a)(ii). Define any further notation that you use.

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