Question

2. We would like to compare the lifetime of four brands of pens. It is suggested that the writing sur- face might affect lifetime, so the following lifetimes in minutes) are collected for each brand-surface combination: Writing Surface 2 3 Brand of Pen 1 2 3 4 709, 659 668, 685 659, 685 698, 650 713, 726 722, 740 666, 684 704, 666 660, 645 692, 720 678, 750 686, 733 (a) Fill in the following ANOVA table: SS df MS F Row Column Interaction Error Total (b) Is there an effect on the lifetime of pen due to the brand (ie, row effect)? Conduct the appropriate test at a = 5%. (e) Is there an effect on the lifetime of pen due to the writing surface (i.c. column effect)? Conduct the appropriate test at a = 5%. (d) Is there an interaction effect on the lifetime of pen due to both the brand and the writing surface? Conduct the appropriate test at a = 5%.

Answer 1

Solotion: @ The nvovA table is The gien ro blem come under mixed effects nodel for factr A Null hypohis HoA 2 >chyo Aematve hy pothe for factorB Noll hypothesi: toa Aternatve hyrothis it forinteractin pull hyrothais :HoAB Alternative hypothesis: e

Two-way ANOVA: Response versus Pen, Surface Source DF SS MS F P Pen Surface 3 1387.5 462.50 0.68 0.583 2 2888.1 1444.04 2.11 0.164 Interaction 6 8100.3 1350.04 1.97 0.149 Error 12 8216.0 684.67 23 20591.8 Total R-Sq (adj) = 23.53% R-Sq = 60.10% S 26.17

I tHere eect on lifertire t pen due to brand ats hm obtaired minitab outpot the tert Statistic vale Cored ponding to the Yow variable Cerand of pen) i F 0.68 and-the pvalue 1 o.r83- The pralue t grater than the signrfrante level of 6.05 ttai to ject null hy pothe ia rgnifont Tharcfme,itcanbe Concludad that there is no drterence between the -four Branda of pent eppect on fetne of pen duet witing Sface 3 fom obtained mintab output, the -tet stahishic Value Caresponding to the Column variable loitng Surface)is F= 2 and pvalve i o.1y. .The pvaue is greater than the signiance level

tfail ject noll hypothe Therefore, it Can be condwded that there no Surfacey diference between he 3 uitng Signitrant an ndraGtran efeet on etime ef pep duCto boh brand and atin Surface at-). Prom obtained minitab output , e dett statistrc Value Carespon ding to the intera chren i F1.9A and te pvalue o 149 The pralue graoter than the ignifrant level ofoor bfailsto reject noll hypothesit and Pen Therefore the Combinatian t brand of Surface doe not afect lrfetine sgnifrantly Intra tion betueen band and coting Syrtace hag no ignidcant effect on etime s Pen. Hene, reiter o em hasa Signfcant efet on ci ehine