n an experiment to see whether the amount of coverage of lig

n an experiment to see whether the amount of coverage of light-blue interior paint depends either on the brand of paint or on the brand of roller used, 1 gallon of each of four brands of paint was applied using each of three brands of roller, resulting in the following data (number of square feet covered).

Roller Brand

1

2

3

1

404

396

401

Paint Brand

2

396

394

397

3

389

392

394

4

394

387

393

a.    Construct the ANOVA table.

c.     Repeat part (b) for brand of roller.

d.    Use Tukey’s method to identify significant differences among brands. Is there one brand that seems clearly preferable to the others?

Justify your answers.

Solution

Ho(paint brand): there is no significant difference of means among brands of paint.

H1(paint brand): there is significant difference of means among brands of paint.

Ho(roller brand): there is no significant difference of means among brands of roller.

H1(roller brand): there is no significant difference of means among brands of roller.

Total sum of squares(TSS)=[404²+396²+401²+.........+387²+393²]-[(4737)²/12]=1870169-1869930.75=238.25.

Row sum of squares(paint brand)=[(1201)²+(1187)²+(1175)²+(1174)²]/3-[(4737)²/12]=1870090.333-1869930.75=159.5833.

Column sum of squares(roller brand)=[(1583)²+(1569)²+(1585)²]/4-[(4737)²/12]=38

Error sum of squares(ESS)=TSS-RSS-CSS=238.25-159.5833-38=40.6667.

At 5% level of significance with (3,6) is F=4.7571 and (2,6) is F=5.1433.

Fcal(paint brand)>Ftab, so we reject Ho(paint brand),

Fcal(roller brand)<Ftab, so we accept Ho(rollet brand)

(b): Tuckey\'s test(q_s)=(Ybar_max-Ybar_min)/(S*(2/n))=(1579-1184.25)/(2.6947*(2/7))=394.75/1.4403=274.0748.

Table value of Tuckey\'s test(q_s)=[(1-alpha),4,[(7-1)*4*3]]=(0.95,4,72)=3.7195.

Here qcal>qtab , so we reject null hypothesis, i.e., there is significant difference among brands.