For hints and examples of similar problems, see last year's Assignment #3 and its solutions.
Use R to re-draw Figs. 8-11, 8-15 and 9-4 from the text.
(a) Carry out an appropriate analysis for the following data, including one or more graphs. State any assumptions you make. As far as possible, test each assumption. State your conclusions.
A sample of surface soil and subsoil was taken from eight randomly selected agricultural locations in a particular county and analysed for surface pH and subsoil pH.
Location:
1
2
3
4
5
6
7
8
Surface pH:
6.55
5.98
5.59
6.17
5.92
6.18
6.43
5.68
Subsoil pH:
6.78
6.14
5.80
5.91
6.10
6.01
6.18
5.88
(b) List some possible sources of variation in the data in (a).
(c) If you want a 95% confidence interval for the mean difference to be ±0.03 units, how large a sample would you need?
Samples of four different brands of diet margarine were analysed to determine the percentage of physiologically active polyunsaturated fatty acids (PAPFUA). Give an appropriate analysis, including an ANOVA table and a graph. Give a 95% confidence interval for the residual variance. State any assumptions you make and do what you can to test the assumptions. State your conclusions.
Brand PAPFUA (%) Imperial: 14.1 13.6 14.4 14.3 Parkay: 12.8 12.5 13.4 13.0 12.3 Mazola: 16.8 17.2 16.4 17.3 18.0 Fleischmann's: 18.1 17.2 18.7 18.4
The following experimental data show steel weight loss (g/m2) as a function of SO2 deposition rate (mg/m2/day).
SO2 deposition rate:
14
18
18
40
43
43
43
45
112
Steel weight loss:
280
350
330
470
500
490
470
560
1200
(a) Fit a straight line to the data by least squares, with weight loss as the dependent variable. Plot the data and the fitted line on a graph. Can weight loss be predicted as a linear function of deposition rate? Present your analysis in an ANOVA table with F-Tests for non-linearity and for the slope of the regression line. Give a 95% confidence interval for the residual variance. State your assumptions and your conclusions.
(b) Predict the weight loss to be obtained at deposition rates of 43 and 80 mg/m2/day. How reliable do you think your predictions are?
13-9 (p. 640). [Hint: you did the interaction plots for (b) in Assignment #1.]