3. The model for a full factorial 24 experiment is: y = 54 13x1 +14x2 + 52x3 - 19x4 + 2x12 - 6x13+5x14 1x23+5x24 8x34 where the coefficients shown are the parameters. If a 24-1 experiment was built with gener- ator 4123, then what terms could be modeled and what would the coefficients become?

3. The model for a full factorial 24 experiment is: y = 54 13x1 +14x2 + 52x3 - 19x4 + 2x12 - 6x13+5x14 1x23+5x24 8x34 where the coefficients shown are the parameters. If a 24-1 experiment was built with gener- ator 4123, then what terms could be modeled and what would the coefficients become?

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter7: Applying Fractions

Section: Chapter Questions

Problem 33MS

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A dairy farmer thinks that the average weight gain of his cows depends on two factors: the type of grain that they are fed and the type of grass that they are fed. The dairy farmer has four different types of grain from which to choose and three different types of grass from which to choose. He would like to determine if there is a particular combination of grain and grass that would lead to the greatest weight gain on average for his cows. He randomly selects three one-year-old cows and assigns them to each of the possible combinations of grain and grass. After one year he records the weight gain for each cow (in pounds) with the following results. Is there sufficient evidence to conclude that there is a significant difference in the average weight gains among the cows for the different types of grain? Cow Weight Gain (Pounds) Grass A Grass B Grass B Grain A 359359 327327 232232 277277 250250 163163 191191 304304 216216 Grain B 331331 348348 176176 318318 205205…
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A dairy farmer thinks that the average weight gain of his cows depends on two factors: the type of grain that they are fed and the type of grass that they are fed. The dairy farmer has four different types of grain from which to choose and three different types of grass from which to choose. He would like to determine if there is a particular combination of grain and grass that would lead to the greatest weight gain on average for his cows. He randomly selects three one-year-old cows and assigns them to each of the possible combinations of grain and grass. After one year he records the weight gain for each cow (in pounds) with the following results. Is there sufficient evidence to conclude that there is a significant difference in the average weight gains among the cows for the different types of grain? Cow Weight Gain (Pounds) Grass A Grass B Grass B Grain A 359359 327327 232232 277277 250250 163163 191191 304304 216216 Grain B 331331 348348 176176 318318 205205…
In an experiment examining human memory, two groups of participants are used. One group is allowed 5 minutes to study a list of 40 words and the second group is given 10 minutes of study time for the same list of words. Then, both groups are given a memory test, and the researcher records the number of words correctly recalled by each participant. For this experiment, identify the independent variable and the dependent variable.
Psychologists at Disney World measured factors that affect the scariness of the soundtrack for their Haunted House ride. In particular, they were interested in the loudness of the screams (soft versus loud) and the length of the screams (short versus long). They used a 2 × 2 factorial design to test how these factors combined. They collected data from 10 different riders in each of the four conditions. Each rider rated the scariness of the ride on a nine-point scale. short screams long screams soft screams T=38, n = 10, SS = 13.6 T=64, n = 10, SS = 22.4 loud screams T=52, n=10, SS = 29.6 T=50, n=10, SS = 16.0 For these data: G = 204, N = 40, X2 = 1156. 1. Sketch a dataplot of the mean rating in each condition. 2. Calculate SS total, the total sum of squares 3. Calculate SSwithin, the within-treatments sum of squares. 4. Calculate SSbetween, the between-treatments sum of squares. 5. Calculate SSA the sum of squares for Factor A (length of scream). 6. Calculate SSB, the sum of squares…
10.5) Assume a pond contains 90 fish: 70 orange, 19 silver, and 1 red. A contestant pays $0.55 to randomly catch one fish and receives $0.35 if the fish is orange, $1.15 if the fish is silver, and $15.00 if the fish is red. How much (on average) does the carnival gain on each play? (If the carnival looses money, enter a negative dollar amount)
6.5. An engineer is interested in the effects of cutting speed (4), tool geometry (B), and cutting angle on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2³ factorial design are run. The results are as follows: (b) (c) (d) (e) B с Treatment Combination (1) b ab ac be abc I 22 32 35 55 44 40 60 39 Replicate II 31 43 34 47 45 37 50 41 III 25 9 50 46 38 3647 29 54 Estimate the factor effects. Which effects appear to be large? Use the analysis of variance to confirm your conclusions for part (a). Write down a regression model for predicting tool life (in hours) based on the results of this experiment. Analyze the residuals. Are there any obvious problems? Based on the analysis of main effects and interaction plots, what levels of A, B, and C would you recommend using?