A file on DocDepot in the assignments folder on doc-depot called bmi.mtp contains data on the Body Mass Index (BMI) of a population of Ottawa residents. The first column identifies the gender of each respondent (1 denotes male and 2 denotes female). The third and fourth columns ‘unstack' the data by male and female BMI.

(a) Treating this set of data as the population, use Minitab to calculate the population mean BMI for male residents. Set aside all population information until part d.

(b) Now use Minitab (Calc Menu - Random Data - Sample from Columns) to draw twenty samples of size n = 30 from the male BMI 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). Using each sample, use Minitab to calculate a 95% confidence interval estimate for the population mean, assuming you do not know the population standard deviation (this interval estimation can be done in one operation on all twenty columns).

(c) For the first sample, confirm the Minitab generated interval by calculating the interval manually.
Display the sample data graphically and comment on whether the relevant assumption regarding the population distribution is warranted (state clearly the assumption needed to justify the interval estimation).

(d) Count the number of intervals that contain the true value of the population mean from part a.

(e) What is the probability you would get the same count in (d) if you took another twenty samples and repeated the above procedures? Show your calculations manually.