An experiment was conducted to study the effect of floor space and feeder trough

Question

An experiment was conducted to study the effect of floor space and feeder trough space on pig growth. A total of 40 pens of pigs were randomly assigned to four treatments in a completely randomized fashion with 10 pens per treatment. The four treatments considered were low floor space (0.3 m^2/pig) and low feeder trough space (2 cm/pig) low floor space (0.3 m^2/pig) and high feeder trough space (4 cm/pig) high floor space (0.6 m^2/pig) and low feeder trough space (2 cm/pig) high floor space (0.6 m^2/pig) and high feeder trough space (4 cm/pig). The treatments were imposed for 13 weeks beginning when pigs reached 17 days of age. The average weight gained (in kg) by the pigs in each pen was used as the response variable. Name the two factors in this study. What are the levels of each factor in this experiment? What are the experimental units in this experiment? The usual one-way ANOVA model was fit to the data from the experiment. The error sum of squares was 555.6. The treatment means (in kg) were as follows: FLOOR SPACE FEEDER high low TROUGH high 61.0 55.8 SPACE low 58.8 56.4 Is there any evidence that the treatments affected weight gain? Conduct one test to answer this question. Show all your work. Is the effect of the floor space the same for both levels of the feeder trough space? Conduct a test to answer this question. Show all your work. Is there a significant interaction between feeder trough space and floor space? Clearly explain and draw a graph of the data (by hand) which illustrates the evidence or lack of evidence of a significant interaction. Regardless of your answer in part (3f), assume there is no significant interaction between the two factors in this experiment. Estimate the main effect of floor s pace. Compute the estimated standard error for the main effect of floor space. Show all your work.

Explanation / Answer

a)

floor space and feeder triugh space

b)

floor space has two levels- high and low

feeder trough space has two levels-low and high

c)

pens of pigs

d)

we reject null if F is greater that F_alpha(1,39)

df adj sum of squares F Floor size SSFloor 1 13.323 13.323*37/2.3975 feeder size SSFeeder 1 0.9025 .9025*37/2.3975 error SSE 37 2.3975 total 39   16.628

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