1. (a) Define the following terms: homoscedasticity, parameter, statistic, pivotal quantity. [4 marks]

   (b) In general, how do you derive a test statistic from a pivotal quantity? Give an example. [4 marks]

2. What is the advantage of computer simulation over biomonitoring to determine childrens' exposure to arsenic from pressure treated wood on decks and play structures? Why must the simulations be random rather than deterministic? [2 marks]
    
3. If x1 and x2 are two independent vectors of observations, what does the following R code compute? [5 marks]

   > lefttail <- pf(var(x1)/var(x2), length(x1)-1, length(x2)-1)
   > ifelse(lefttail < 0.5, 2*lefttail, 2*(1-lefttail))

4. Analyse the following two data sets with appropriate graphics and P-values. State your assumptions and your conclusions. Wherever possible, assess the validity of your assumptions. [30 marks]

   (a) In an experiment to study the effects of liming and urea fertilizer application on dimethoate (a pesticide) retention by loamy soil, the following percentages of dimethoate recovery were observed in 10 independent samples.

   Soil treated with lime:  28.5  24.7  26.2  23.9  29.6
   Soil treated with urea:  38.7  41.6  35.9  41.8  43.2

   (b) Zinc concentration (mg/L) was measured for both surface water and bottom water at six different locations along a river. Do the data suggest that average zinc concentration is higher for bottom water than for surface water?

   Location:      1      2      3      4      5      6
   Bottom:    0.430  0.266  0.567  0.531  0.707  0.716
   Surface:   0.415  0.238  0.390  0.410  0.605  0.609

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Statistics 3N03/3J04