F11 5. (30 points) Olive & Marius published recently in the Journal of Improbable Experimental Data, an interesting paper in which they compare the consumption of (stale) pop corn (measured in grams) as a function of the size of the bucket in which the pop corn was presented (they used two sizes: large and small). Olive & Marius ran their experiment in four different (randomly chosen) movie theatres because these authors were wondering if the localization of the theatre could have an influence on the effect of the size of the bucket. They mentioned that they tested a total of forty subjects and that the within group mean square was equal to 100. They report their results in the following table: A: Movie Theatres #1 #2 #4 Marginal #3 Means B Big Bucket 39 41 41 39 40 Small Bucket 19 29 15 20 17 Marginal 30 Means 29 29 35 27 a. What is the dependent variable? b. What is/are the independent variable(s)? Indicate for each if it is fixed or random (justify your answer). C. What are the total number of levels in the experiment? d. How many subjects are included in each level of the experiment?Tne Salsa , . Compute the values of the effects for A and write them in this table contrast Al A2 A3 A4 He f. Compute the values of the effects for B and write them in this table B1 B2 9. Compute the values of the effects for the interaction AB and write them in this table A4 A3 A1 A2 B1 B2 h. What are the expected values of the mean squares for this design (give the right notations)? The authors hypothesize that people who get big buckets will consume more popcorn than people who get small 2. buckets (irrespective of the theatre). Convert this hypothesis into a contrast (include all levels of the experiment).ediday F12 Build back only the omnibus ANOVA table (exclude any contrasts), and indicate whether the F-ratio(s) is/are statistically significant at a = 0.05. K Source df SS MS F V1 , U2 Foritical Total . State all the conclusions reached by the authors based on only the omnibus ANOVA (Note: the Journal of Improbable Data uses APA style)? the