53. A study was carried out to compare the writing lifetimes of four premium brands of pens. It was thought that the writing surface might affect lifetime, so three different surfaces were randomly selected. A writing machine was used to ensure that conditions were otherwise homogeneous (e.g., constant pressure and a xed angle). The accompanying table shows the two lifetimes (min) obtained for each brand—surface combination. In addition,

 , and  .

Writing Surface Brand of Pen 1 2 3 xi..

1 709, 659 713, 726 660, 645 4112 2 668, 685 722, 740 692, 720 4227 3 659, 685 666, 684 678, 750 4122 4 698, 650 704, 666 686, 733 4137 x.j. 5413 5621 5564 16,598 Carry out an appropriate ANOVA, and state your conclusions.