The file medinc.mtw contains data on the median incomes (medinc) of census dissemination areas in Toronto. (a) Treating this set of data as the population, use Minitab to calculate the population mean and the population standard deviation for the medinc variable. Set aside all population information until parts (d) and (e).

(b) Use Minitab (Calc Menu Random Data Sample from Columns) to draw twenty samples of size n = 40 from the Toronto medinc population. This procedure must be replicated twenty times (note that if you open up the same sampling dialog box each time from the menu, then you only have to replace the last destination column with the next one. In Minitab Express, you must specify the sample size each time but you do not need to specify the destination column). For each sample, use Minitab to calculate the sample mean. Note that when you can use the Descriptive Statistics function, you can specify the calculation of only the sample means of all your samples at once.

(c) Copy the sample means into a new column and calculate the mean and standard deviation of your sample means.

(d) The sampling distribution of the sample mean has an average equal to the population mean. Explain why the mean in part (c) may be different from the population mean in part (a).

(e) How would you use the sample standard deviation in part (c) to estimate the population standard deviation in part (a)? How close is your estimate to the true value?

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