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General Instructions: For all problems you should create appropriate graphs to evaluate all assumptions and provide a visual comparison of the treatment effects. Since the computer is doing the computations, it is important that you clearly interpret all results in the context of the problem. Don’t just say the F test is significant. Explain what that means in terms of the treatments being studied. 1) Stereograms appear to be composed of random dots. However, they contain separate images that a viewer can “fuse into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An experiment was conducted to determine if knowledge of the form of the embedded image affected the time required to fuse the image. Subjects were randomly assigned to two groups, the NV group received no information about the image and the VV group received both verbal and visual information about the image. The times required to fuse the image were recorded in file T1P1.csv. Conduct a test to see if there is a difference and determine a confidence bound for the difference. Interpret the results. 2) A manufacturer conducted a small pilot study of the effect of the price of one of its products on sales of this product in hardware stores. Sixteen stores were used in the study with four in each of the four geographical regions and one of each size in each region. Four price levels were used in the study and were assigned to the stores so that each price level was assigned to each combination of region and store size. Identify the type of design used and analyze the data in file T1P2.csv to see if there is an impact on sales, and if there is, identify the nature of the impact. 3) A physiologist studied the effects of three reagents on muscle tissue in dogs. Ten litters of three dogs each were randomly selected and the three reagents were randomly assigned to the three dogs in each litter. The data from the experiment are in file T1P3.csv. Identify the type of model and analyze the data to see if there is a difference between reagents. If there is a difference, conduct an appropriate multiple comparisons procedure to identify the differences. 4) A rehabilitation center was interested in the impact of fitness level at the start of therapy to the time in physical therapy required to complete rehabilitation. Data were collected for 24 patients who had undergone a similar corrective knee surgery and the individuals were ranked on their fitness level as 1 — below average, 2 — average, and 3 — above average.the number of days required for physical therapy for each individual are in T1P4.csv. Prepare a comparative graphical analysis of the data and conduct an ANOVA to test if there is a difference in mean recovery time. 5) An engineer is studying the mileage performance characteristics of five types of gasoline additives. In the road tests cars are to be used as blocks, there is only enough time to run four of the five additives in each car. The mileage data for this experiment are in file T1P5.csv. What type of design is this? Conduct an analysis to identify whether some additives are better than others.
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