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Question 1: A group of students have performed a two-level factorial experiment where they investigate how the factors (temperature (T) amount of water (W) and amount of light (L) influence the growth of a certain type of plants. For each combination of factor levels, they have 3 repetitions of experiment, and their initial results are given in the table below: Factor Temperature (9 Amount of water (9) Amount of light (hourſday) Symbol T w L Level (141) 25 35 100 300 2 8 TXW 45 TXL L -1 WXL 1 T -1 1 -1 -1 -1 -T 1 1 -1 1 -1 1 Growth length (mm) 55 1.3 4.0 13 02 15 40 102 -1: -1 NINIS -1 Run 1 2 3 4 5 6 7 8 Average + Average Effect 1 - 1 -1 1 1 -1 1 -1 1 1 1 1 1 1 b. Construct main effect plots for the main factors used in the experiment, and discuss main factor settings that can be used to improve the growth length (30%) e Construct interaction plots for TXW and Wxl, and discuss, based on the interaction plot, the evidence that any of these interactions have an effect on the growth length (40%) d. Write a prediction equation for the growth length and predict the maximum value of the growth length' response and discuss the results (30%)
Question 2: Fifteen adult males between the ages of 35 and 50 participated in a study to evaluate the effect of diet and exercise on blood cholesterol levels. The total cholesterol was measured in each subject initially and then 5 months after participating in an aerobic exercise program and switching to a low-fat diet, as shown in the table below. People Varianc 2 3 5 67 8 4 9 10 Before 264 241 258 295 251 245 286 314 260 279 555.57 Alter 228 232 227 240 238 241 234 256 247 239 76.84 (a) Calculate the (before and after) sample mean and standard deviation; [20%) (b) Calculate other relevant sample statistics, i.e. median, 1" and 30 quartiles, range and inter-quartile range, (40%) (c) Construct a comparative box-plot for "before and after cholesterol data and discuss your observations; [20%) (d) Use tally charts / counts to calculate frequencies (use 5 bins) and construct histograms for the 2 sets of data, (20%)
Question 3: The table below shows the result of an experimental study conducted by a group of civil engineering students on the coefficient of thermal expansion (a) of a steel structure. Temperature 60 50 [°C] 40 30 20 10 0-10-20-30-40-50-60 a [mm/mm °C) 7.3 7.2 716.8 6.6 5.4 6.3 6.2 6.0 5.9 57 55 5.3 (a) Draw a scatter diagram of the coefficient of thermal expansion (a) against temperature (T). Comment the plot and suggest an equation that seems appropriate in relating a to T? (30%) (b) Using linear regression to determine the relation between thermal expansion and the temperature. [40%) (c) Using the regression equation from (b) to calculate the regression residuals for each experimental point and construct a run chart plot for these residuals. Discuss the residual plot commenting on relevant features [30%)