Question

Feel free to use Minitab or Excel on all aspects of this.

a) Collect a sample of n=50 data values for which you can observe some variation. Describe the source of the data, that is, how did you get it? (If all the data are the same with no variation, you aren’t measuring carefully enough).

b) Make a histogram of your 50 data values, and comment on the location, spread and shape.

c) Calculate the mean and standard deviation of your 50 data values.

d) Develop a normal probability plot of the 50 data values. What do you conclude from the plot? Is your data normally distributed? If not, try some other distributions from the pulldown menu in Minitab and see if you can find a good fit.

e) Collect 15 random samples, each of size n=5, from your 50 data values. (You could do this by writing each of the 50 data values onto small pieces of paper, and randomly selecting 5 of them from a bag.) After taking your sample of 5 measurements, compute the mean (X-bar). Put the five values back and mix them up before taking your next sample. Repeat this until you have 15 samples averages. (Sorry, I know this is tedious). Develop a histogram of the 15 sample averages. What do you notice about the histogram? How does it differ from the one in part b?

f) Develop a normal probability plot of the sample averages. Are your X-bars normally distributed? What does this plot reveal?

g) Calculate the mean and standard deviation of your 15 X-bars. How do these compare with the mean and standard deviation of the original sample of 50 individual items?

Answer 1