Total fat content (including saturated fat and trans fats) is a key characteristic of cheese. Assume that for a given type of cheese, total fat content (10-1 g/g of cheese) follows a normal distribution with a population mean of 2.85 (unit) and a population variance of 0.01 (unit2). Such an assumption is reasonable because fat content varies inside cheese and the “errors” around the mean total fat content (i.e. the value appearing on the etiquette) are distributed like a bell shape. Twenty-five (non-statistical) samples of 1 g of cheese drawn from the same container were analyzed for total fat content. In other words, an i.i.d. random sample of size 25 was collected from a normal population of cheese total fat contents with the parameter val
Total fat content (including saturated fat and trans fats) is a key characteristic of cheese. Assume that for a given type of cheese, total fat content (10-1 g/g of cheese) follows a
Twenty-five (non-statistical) samples of 1 g of cheese drawn from the same container were analyzed for total fat content. In other words, an i.i.d. random sample of size 25 was collected from a normal population of cheese total fat contents with the parameter values given above.
a) Calculate the median of the sample variance.
b) What is the minimum value of n required for the mean total fat content of n samples of 1 g of cheese, to differ from the population mean by more than 0.01 (unit) with a probability of 0.10?
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