Calculate and plot the mean and standard-deviation

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Reference no: EM131372626

1) Determine manually the lower and upper limits on sample standard deviations, using your own population's (μ, σ) for (1- α) = 0.95 and sample sizes of n = 5, 20. 80. and 320.

2) Use your own random (μ, σ) to generate four sets of (normal-distribution based) random numbers (i.e., samples) of sizes n = 5, 20, 80, and 320, respectively.

3) Calculate the means and standard deviations for the 4 samples you generated in Point-2 above. Ensure that these are within the limits found in Point-1, otherwise, repeat Point-2 and replace the data set(s).

The Normal Distribution - Estimation Theory

4) Now, assume that (μ, σ) are unknown. Estimate the four pairs of different 95% confidence intervals, for the population's statistics (Ica). using the four samples' data in Point-3 above, respectively.

5) Plot your results found in Point-4 above as (p versus n) and (a versus n), (i.e., two limit points for every n value), and include reference lines at the true population statistics values. Explain, in two or less sentences, your observations. (Note that your own (μ, σ) selected in Point-1 above are the true values for the population statistics).

The Normal Distribution - Statistical Process Control

6) Use all the 80 points of the n = 80 data set in Point-2 above to create 20 sub-set samples of size n = 4 each.

7) Determine the ±3σ control limits, both for sample-mean and -standard-deviation (i.e., X-Bar and S) charts, using the sample data in Point-6 above.

8) To simulate a potentially out-of-control process, change your own original μ and σ (Point-1 above) as (μ* =K1xμ, σ* =K2xσ), i.e., calculate a new set of population statistics, where K1 and K2 are two separate randomly generated values: K1 is between 2.1-2.3, and K2 is between 1.5-2.0, respectively.

9) Generate a new set of 20 samples all of size n = 4, using the new population statistics (Point 8). μ* and σ*.

10) Calculate and plot the mean and standard-deviation data for the 20 new samples (Point-9 above) on the X-Bar and S charts using the control limits calculated for the population with the original (μ, σ) values (Point-7 above). Explain, in two or less sentences, your observations.

Reference no: EM131372626

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1/27/2017 1:56:17 AM

Show at least one sample calculation for calculating limits. Attach screen capture of generated numbers in the appendix. This is done in Minitab, but you can calculate by hand to confirm the intervals are correct. Remember to include values in the summary. Include plots in the appendix. Remember to comment in the summary. Include plots in the appendix; comment and outline results in the summary. Show K values in the summary. Add new set of values to the appendix. Add plots to the appendix. Comment in the summary. Variables & Nomenclature: All variables must be correctly labeled. Variables mentioned in the summary must be clearly defined. Significant figures should be chosen logically and correctly. Report Writing Program: Any word-processing software may be used to write the report.


1/27/2017 1:56:08 AM

Your answers, obtained using ONLY and exclusively the MINITAB software, except where clearly stated otherwise, must be according to formulae and concepts introduced. Must include a maximum 2-page summary, plus unlimited number of pages of appendices, containing solutions to Questions 5b-14 below, plots, and data tables. Page limit: All questions must be answered, or commented on, within the 2-page limit. All graphs and screen-prints (from Minitab only) should be included in an appendix. Answering Questions: All mathematical work (where applicable) should be clearly displayed, with derivations if necessary.

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