. The strength of five types A, B, C, D and E of fibre­board were being compared. Four boards of each type were tested. The modulus of rupture of each of the 20 boards is given in the following table: A B C D E 619 424 392 462 465 674 525 494 559 568 633 549 441 556 613 622 601 457 611 611 a. Use Bartletts test to determine if the within board variances are significantly different (α = 0.05). b. Perform analysis of variance and draw your conclusions (α = 0.05). c. Use Bonferronis Multiple Comparison Test, with a 0.05 level of significance, to compare the means. Discuss your results. d. Calculate 95% confidence limits for the difference of means D and E 2. The following are the yields in kilograms of above­ground biomass per plot that resulted when four levels of nitrogen were applied to young Douglas­fir seedlings. Treatment N0 N1 N2 N3 4.37 7.50 7.80 9.40 6.72 8.80 7.82 9.28 8.32 8.73 9.62 8.03 9.00 a. Construct the analysis of variance table (α = 0.05). b. Calculate 95% confidence limits for the mean of treatment N2 . 3. An experiment was set up to test the production of women against the production of men in forest inventory cruising. The data below show the number of plots they put in per day in three different forest types (A, B, C) for four randomly selected working days. Number of plots per day in types: 6/28/2015 Assignment Instructions – 2015SA-FRST231-... Women 5 8 8 6 6 8 8 6 8 5 8 10 7.17 Men 9 8 10 7 7 7 9 9 8 11 8 7 8.33 Average 7.5 7.5 8.25 7.75 a. Analyze the experiment (using a= 0.05 for level of significance) and draw your conclusions. b. Calculate 95% confidence limits for the mean of women in Type C. c. Calculate 95% confidence limits for the mean of men. Simple Linear Regression 1. The radius of the crown (in metres) and the diameter at breast height (in centimetres) were measured for ten Sitka spruce trees. dbh (cm) Crown Radius (m) X Y 5.0 0.91 12.7 1.83 7.6 1.22 17.8 1.83 5.1 1.22 6/28/2015 Assignment Instructions – 2015SA-FRST231-... 15.2 2.44 10.2 1.70 22.9 2.74 20.3 2.65 10.1 1.52 a. Plot the observations to check if the linear relationship is reasonable. b. Fit a linear regression of Yi = b0 + b1 Xi c. Test if the linear regression is significant. d. Compute the correlation coefficient and the coefficient of determination and discuss their meaning. e. Calculate Standard Error of Estimate and explain its meaning. f. Calculate 95% and 99% confidence limits for the slope and intercept. Discuss your results. g. Calculate the average crown radius for all 17.0 cm trees with 95% confidence limits and discuss your results. h. Is your average radius calculated for 16.0 cm trees significantly greater than 1.5 metres (α = 0.05)? i. Is your intercept significantly greater than zero? Use α = 0.05