Question # 1:

Prior to submitting a bid for a construction job, cost engineers prepare detailed analysis of the estimated labor and materials costs required to complete the job. This estimate will depend on the engineer who performs the analysis. An overly large estimate will reduce the change of acceptance of a company's bid price, whereas an estimate too low will reduce the profit or even cause the company to lose money on the job. A company that employs three job cost engineers wanted to compare the mean performance of the engineer's estimates for the same four jobs. The data is in CostEng; the estimates are in hundreds of thousands of dollars. Perform an analysis on the data to determine if the estimate was impacted by the engineer conducting the estimate.

Engineer: 1,1,1,1,2,2,2,2,3,3,3,3

Job: 1,2,3,4,1,2,3,4,1,2,3,4

Cost: 4.6,6.2,5.0,6.6,4.9,6.3,5.4,6.8,4.4,5.9,5.4,6.3

a. What is the dependent variable? (1 point)

b. What is the independent variable? (1 point)

c. What is the covariate? (1 point)

d. Does the covariate statistically predict the dependent variable? Explain in one sentence. (2 points)

e. Was the estimate impacted by the engineer conducting the estimate? (1 point)

f. The amount of variation due to the engineer is how many units? (1 point)

g. The amount of variation due to the job estimated is how many units? (1 point)

A marketing manager for a certain well-known drinks manufacturer was interested in the therapeutic benefit of certain soft drinks for curing hangovers. He took 15 Ohio University college students out on the town one night and got them drunk. The next morning as they awoke, dehydrated and feeling ill, he gave five of them water to drink, five of them Gatorade and the remaining five a cola brand (Variable Drink). He then measured how well they felt (on a scale of 0 = I feel like death to 10 = I feel really healthy) two hours later (Variable Well). He wanted to know which drink produced the greatest level of wellness. However, he realized it was important to control for how drunk the student got the night before, so he measured this on a scale of 0 = as sober as can be to 10 = wasted (Variable Drunk). The data is in HangoverCure. Conduct an ANCOVA to see whether the students felt better after drinking drinks when controlling for how drunk they were the night before.

Drink: 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,

Well: 5,5,6,6,3,5,4,6,8,6,5,6,6,6,6,

Drunk: 5,3,2,1,7,6,6,4,2,3,2,3,2,3,2

a. Run an ANOVA and determine if the variable drink had a statistically significant impact on the variable well. Explain in one sentence. (2 points)

b. Are the independent variable and the covariate independent? Explain in one sentence. (2 points)

c. Has the assumption of homogeneity variances been met for the ANCOVA test? Explain. (2 points)

d. Does the covariate significantly predict the dependent variable? Interpret in one sentence. (2 points)

e. Does the type of drink predict the dependent variable when drunkenness is removed? Explain in one sentence. (2 points)

f. Running contrasts to compare Water vs. Gatorade and Water vs. Cola, one of the comparisons is significant. Which comparison is significant? Explain in one sentence. (4 points)

g. Reviewing the regression parameter estimates, we can determine the comparison between the reference category cola (Drink = 3) with Gatorade by looking at the mean difference in Drink = 2. Is this comparison significant? Explain. (2 points)

h. What is the partial eta square for the variable drink? (1 point)

i. What is the partial eta square for the variable drunk? (1 point)

j. Which of the two variables explains a bigger proportion of wellness? (1 point)

k. Which drink should you recommend to cure hangovers? Explain. (4 points)