structural engineer is studying the strength of aluminum alloy purchased from three vendors

1. A structural engineer is studying the strength of aluminum alloy purchased from three vendors. Each vendor submits the alloy in standard-sized bars of 1.0, 1.5, or 2.0 inches. The processing of different sizes of bar stock from a common ingot involves different forging techniques, and so this factor may be important. Also, the bar stock is forged from ingots made in different heats. Each vendor submits two test specimens of each size bar stock from three randomly selected heat levels (these levels are different for each of the vendors).

Vendor 1                  Vendor 2                    Vendor 3  

b) Construct an ANOVA table including the expected mean squares in tabular form as shown below. State the null and alternative hypotheses for all effects, test each of the hypotheses, and interpret your results. Use α = 0.05. {4 points}

Source df SS MS EMS

2. A researcher studied the effects of three experimental diets with varying fat contents on the total lipid (fat) level in plasma. Total lipid level is a widely used predictor of coronary heart disease. Fifteen male subjects who were within 20 % of their ideal body weight were grouped into five blocks according to age. Within each block, the three experimental diets were randomly assigned to the three subjects. Data on reduction in lipid level (in grams per liter) after the subjects were on the diet for a fixed period of time follow: 

 (a) Why do you think that age subject was used as a blocking variable?(3 points)

(b) Obtain the analysis of variance table. Does it appear that the treatment means differ? (4 points)

(c) Test whether or not the mean reductions in lipid level differ for the three diets; Use a = 0.05. State the alternatives, decision rule, and conclusion. What is the p- value of the test? (4 points)

(d) Estimate C1 = m·1 - m·2 And C2 = m·2 - m ·3 using Bonferroni procedure with a 95 % family confidence coefficient. State your findings. (4 points)

(e) A standard diet was not used in this experiment as a control. What justification do you think the experimenters might give for not having a control treatment here for comparative purposes? (2 points)

(f) Based on the estimated efficiency measure, how effective was the use of the blocking variable as compared to a completely randomized design?

3. A traffic engineer conducted a study to compare the total unused red light time for five different traffic light signal sequences. The experiment was conducted with a Latin square design in which the two blocking factors were (1) five randomly selected intersections and (2) five time periods. In the data table the five signal sequence treatments are shown in parentheses as A, B, C, D, E., and the numerical values are the unused red light times in minutes. 

(a) Write a linear model for this experiment, explain the terms, and compute the analysis of variance. (5 points)

(b) Compute the standard error for a signal sequence treatment mean and for the difference between two signal sequence treatment means. (3 points)