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# ec8a - The University of Hong Kong Department of Statistics...

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1 The University of Hong Kong Department of Statistics and Actuarial Science STAT0302 Business Statistics Semester 2 2009/2010 Example Class 8 Suggested Solution 1. Let X be the weight of detergent packets (in grams) where 2 ~ , X N   From calculator, we obtain 202.5 x , 2.821620 s and 14 n . (a) An unbiased estimate for is the sample mean 202.5 x . (b) 95% confidence interval for is 1 2 . . 1 s C I x t n n 0.95 0.025 2.821620 . . 13 202.5 2.16 200.87,204.13 14 s C I x t n where 0.025 13 t is such that 0.025 13 0.025 P t t . Look up t test Table, level of significance for two-tailed tests= 0.05 (or level of significance for one-tailed tests= 0.025) and 13 df . This gives 0.025 13 2.16 t Interpretation: there is a 95 % chance that the true but unknown mean falls in the confidence interval (c) Setting up hypotheses: 0 : 204 H v.s. 1 : 204 H This is a two-sided test. The hypothetical value 0 204 lies inside the 95% confidence interval This means that we do not reject 0 H at 0.05 . There is no evidence to suggest that 204 at the 0.05 level of significance. Remarks: part (b) suggests that the true mean exceeds 204.13 with probability 0.025 and that it is lower than 200.87 with probability 0.025. In part (c), the statistical test will reject the null hypothesis if the sample mean is either too large or too small. If the sample mean is larger than b or is smaller than a , the null hypothesis is rejected. These values a and b are specified by the significance level. Given

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