6. [1.4/6.66 Points] PREVIOUS ANSWERS DEVORESTAT9 11.2.022. PRACTICE ANOTHER A study was carried out to compare the writing lifetimes of four premium brands of pens (factor A). It was thought that the writing surface (factor 5) 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. Wr ing Surface 1 2 3 XL. 709, 559 713, 726 660, 645 4112 1 2 658,685 722, 740 592,720 4227 3'3\"\" 3 659,585 665,684 678,750 4122 ofPen 4 698, 650 704, 666 687, 733 4138 5413 5521 5565 16,599 The hypotheses are as follows. , 2 _ . _ _ _ _ . 2 _ H05.aGD HOA.a1a2u3a40H5.a5 -0 Has: 652 > 0 HaA: at least one (1,: 0 Has: 1752 > 0 Carry out an appropriate ANDVA' (Use a = 0.05. Round your answers to two decimal places') Source df 55 MS f A 3 v 7 f1 1,35 5 2 J :1 :1 AB 6 J Error 11 v Total 23 v Test for an interaction' Find the critical value. (Round your answer to two decimal places.) mm :1 State the conclusion in the problem context. O Reject H06. The data suggests that there is an interaction. 0 Fail to reject HOG' The data does not suggest that there is an interaction. 0 Fail to reject HOG' The data suggests that there is an interaction. 0 Reject HDG' The data does not suggest that there is an interaction. Test for a brand effect. Find the critical value. (Round your answer to two decimal places.) mm 1:1 State the conclusion in the problem context. 0 Fail to reject HOA' The data suggests that there is a brand effect. 0 Reject HM. The data suggests that there is a brand effect. 0 Reject HM. The data does not suggest that there is a brand effect