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Q1. Consider the population of adult females resident in Melbourne. Our focus is on the population mean height. Assume we know (population standard deviation) is 25, but we do not know the population mean, μ. We take a sample of adult females resident in Melbourne (n=100) and calculate the sample mean height as 70 cm.
i) Write down the distribution of X, female height.
ii) Write down the distribution of Are you relying on any theorems in your . answer? If yes explain.
iii) Derive the 95% confidence interval around the sample mean.
iv) In your answer to iii) will the specific confidence interval you have derived contain the population mean? Explain carefully.
b. If the forecast in May was 42, develop a forecast for December based on exponential smoothing with α = 0.25. c. For the data set below, determine the bias, the mean squared error and the mean absolute deviation.
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