Statistics 3N03 - Assignment #3

2002-11-23

Due: 2002-12-02 18:00

Use R to do the graphics on this assignment. Do the ANOVA calculations in R and with your calculator, and submit both. The text references are to Montgomery & Runger, Applied Statistics and Probability for Engineers, 2nd edition.

For hints and examples of similar problems, see last year's Assignment #3 and its solutions.

Question 1

Use R to re-draw Figs. 8-11, 8-15 and 9-4 from the text.

Question 2 [2001 Exam Q2]

(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?

Question 3 [2001 Exam Q3]

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
Question 4 [2001 Exam Q4]

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?

Question 5

13-9 (p. 640). [Hint: you did the interaction plots for (b) in Assignment #1.]

Statistics 3N03