1K Q-1: [50] The Swiss psychologist Jean Piaget, known for his work on child development, on + years old from two Swiss Cantons: Ticino and Vaud. He made three boards with nine pictures per board, showed these boards sequentially to a child for 10 or 30 seconds, and asked the child to say where he saw the pictures. The correct locations by a child were technically scored for each board as shown below. 0 A B Run Number 1 2 3 4 5 6 7 Actual run Order 3 8 6 2 7 Score y2 4 2 8 y1 3 2 7 6 5 5 13 Factor Levels y3 Low (-) High (+) 3 A: Ticino Vaud 1 B: 6 years 10 years 8 C: 10 sec 7 Note-1 5 Vaud is pronounced as Vo 4 Note-2 13 Higher score means 30 sec + 6 5 3 12 4 + 1 + [03] a) Determine the number of replicates, treatment combinations, and hypotheses in this experiment. [16] b) Determine the effect estimates, sum of squares, and percent contribution of all model terms, and Construct a half-normal % probability plot of the effect estimates. Which factors appear to have large effects? [15] c) Conduct an analysis of variance using the half-normal % probability plot in part a) for guidance in forming an error term. What are your conclusions? [Use a = 0.05.] [08] d) Write down a fitted regression model relating Score to the important variables in coded form. [08] e) Based on your fitted regression model, what is the expected average score of a 10 year old child from Vaud? How does that compare to the expected average score for a 10 year old child from Ticino? 1K Q-1: [50] The Swiss psychologist Jean Piaget, known for his work on child development, on + years old from two Swiss Cantons: Ticino and Vaud. He made three boards with nine pictures per board, showed these boards sequentially to a child for 10 or 30 seconds, and asked the child to say where he saw the pictures. The correct locations by a child were technically scored for each board as shown below. 0 A B Run Number 1 2 3 4 5 6 7 Actual run Order 3 8 6 2 7 Score y2 4 2 8 y1 3 2 7 6 5 5 13 Factor Levels y3 Low (-) High (+) 3 A: Ticino Vaud 1 B: 6 years 10 years 8 C: 10 sec 7 Note-1 5 Vaud is pronounced as Vo 4 Note-2 13 Higher score means 30 sec + 6 5 3 12 4 + 1 + [03] a) Determine the number of replicates, treatment combinations, and hypotheses in this experiment. [16] b) Determine the effect estimates, sum of squares, and percent contribution of all model terms, and Construct a half-normal % probability plot of the effect estimates. Which factors appear to have large effects? [15] c) Conduct an analysis of variance using the half-normal % probability plot in part a) for guidance in forming an error term. What are your conclusions? [Use a = 0.05.] [08] d) Write down a fitted regression model relating Score to the important variables in coded form. [08] e) Based on your fitted regression model, what is the expected average score of a 10 year old child from Vaud? How does that compare to the expected average score for a 10 year old child from Ticino
