S2MB3 - Assignment #1

Statistics 2MB3 - Assignment #1

2005-01-25

Due: 2005-02-02 18:00

Do all of your graphs and calculations in R. Submit your work as a report, pasting the graphs into a word processor and adding comments and discussion. Numbered exercises are from Devore, J.L. (2004) Probability and Statistics for Engineering and the Sciences, Sixth Edition, Brooks/Cole.

Question 1: Time series analysis

Analyse the time series for PCB in solids at Niagara on the Lake in the Niagara River Pollution Case Study. Give time series plots and lag-1 plots in original units and again in log units. Try smoothing the time series plots using the methods of Ex 82(b) p. 50. Discuss what you have learned from the graphs.

Hints: See S2MA3 2002-2003 Test #1 and solutions, S3N03 2000-2001 Test #1 and solutions .

Question 2: Comparative box plots and stem and leaf plots

Ex 59 p. 47. Also give comparative stem and leaf plots; they don't have to be back-to-back but they should use the same stems.

Question 3: Scatterplot matrix

Use the data from Ex 44 p. 607. Give only a graphical analysis.

Question 4: Interaction plots

Use the data from Ex 22 p. 465. Give only a graphical analysis. You can use the R function interaction.plot() but you also need to know how to draw an interaction plot by hand.

Question 5: Probability plots

Ex 88 p. 198, Ex 91 p. 199.

Question 6: A computer simulation experiment

Generate samples of size n = 10, 50, 100 and 500 from a normal distribution with mean = 3 and variance = 9. Plot each sample as a histogram with the N(3, 9) probability density superimposed. Show each sample on a normal probability plot using qqnorm() and qqline(). Repeat this several times for each sample size, but, to save paper, only put one of each in your report. How large does n have to be before a sample from a normal distribution looks like it came from a normal distribution?

Now generate samples of size n = 10, 50, 100 and 500 from an exponential distribution with mean = 3. What is the variance of this distribution? Repeat the exercise above, comparing the histograms to a N(3, 9) density function and drawing normal (not exponential) probability plots. How large does n have to be before a a sample from an exponential distribution looks like it did NOT come from a normal distribution?