Use the information below to answer question 911 study was d

Use the information below to answer question 9-11 study was done in other to determine how writing surface (Factor A) and pens\' brand (Factor B) affect the lifetimes of pens. Other conditions being held constant, the lifetimes of brand-surface combination are contained in the table below. The partial ANOVA table is also provided. Writing Surface 1709; 659 2 668; 685 3 659; 685 4 698; 650 Brand of Pen 713; 726 722;740 666; 684 704; 666 660; 645 692;720 678; 750 686; 733

Solution

No. of levels for treatments:

Writing surface : a = 3

Brand : b = 4

No. of repetitions = n =2

DF for B = b-1 = 3

DF for interaction = (a-1)*(b-1) = 2*3 = 6

DF for error = a*b*(n-1) = 3*4*(2-1) = 12

9. F stat for interaction: MS interaction / MS Error

= (8100.2 / 6) / (8216 / 12) = 1.972

F critical : F_6,12,0.05 = 3

So, Answer: A

11. F stat for treatment Brand: MS Brand / MS Error

= (1387.5 / 3) / (8216 / 12) = 0.676

F critical : F_3,12,0.05 = 3.50

So, Answer: A