Question

A new diet that promises a fast loss of weight is launched. The change in weight after a week on the diet is modelled using a Normal distribution with mean u and variance σ2. Let z, . . . , zn be an independent sample from this Normal. (a) Knowing that μ z, find the method of moments estimator for σ. [4] (b) State (without deriving) an alternative estimator you know for σ2. Give one reason why one would prefer this second estimator. Explain or prove if needed (c) Use the pivot method to derive the formula for a 100(1-a)% confidence interval for σ2 (d) The weight change of a sample of 6 women following the diet for a week are given below: 0.3,-0.5,-0.4,-0.1,0.2,0.7 Find a 95% confidence interval for σ2 Total 20]

Answer 1

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