Introduction to Probability and Statistics for Engineers and Scientists

10.3One-Way Analysis of Variance 447

p-Values in a One-way ANOVA

Start

Quit

1

2

3

4

5

Sample 1

220

251

226

246

260

244

235

232

242

225

The value of the f-statistic is 2.6009

The p-value is 0.1124

SSW

M*(N−1)= 165.9667

SSB

M− 1 = 431.6667

Sample 2 Sample 3

252

272

250

238

256

FIGURE 10.1

The following represents the total mileages obtained by the different motors:

Gas 1: 220 251 226 246 260

Gas 2: 244 235 232 242 225

Gas 3: 252 272 250 238 256

Test the hypothesis that the average mileage obtained is not affected by the type of gas
used. Use the 5 percent level of significance.

SOLUTION We run Program 10.3 to obtain the results shown in Figure 10.1. Since the
p-value is greater than .05, the null hypothesis that the mean mileage is the same for all 3
brands of gasoline cannot be rejected. ■

The following algebraic identity, called the sum of squares identity, is useful when
doing the computations by hand.

The Sum of Squares Identity

∑m

i= 1

∑n

j= 1

Xij^2 =nmX..^2 +SSb+SSW