Problems 479

(a) Test the hypothesis that there is no interaction between gender and diet.

(b) Test the hypothesis that the diet has the same effect on men and women.

25.A researcher is interested in comparing the breaking strength of different laminated

beams made from 3 different types of glue and 3 varieties of wood. To make the

comparison, 5 beams of each of the 9 combinations were manufactured and then

put under a stress test. The following table indicates the pressure readings at which

each of the beams broke.

Glue

Wood G1 G2 G3

196 208 214 216 258 250

W 1 247 216 235 240 264 248

221 252 272

216 228 215 217 246 247

W 2 240 224 235 219 261 250

236 241 255

230 242 212 218 255 251

W 3 232 244 216 224 261 258

228 222 247

(a) Test the hypothesis that the wood and glue effect is additive.

(b) Test the hypothesis that the wood used does not affect the breaking strength.

(c) Test the hypothesis that the glue used does not affect the breaking strength.

26.A study was made as to how the concentration of a certain drug in the blood,

24 hours after being injected, is influenced by age and gender. An analysis of the

blood samples of 40 people given the drug yielded the following concentrations

(in milligrams per cubic centimeter).

Age Group

11–25 26–40 41–65 Over 65

Male 52 52.5 53.2 82.4

56.6 49.6 53.6 86.2

68.2 48.7 49.8 101.3

82.5 44.6 50.0 92.4

85.6 43.4 51.2 78.6

Female 68.6 60.2 58.7 82.2

80.4 58.4 55.9 79.6

86.2 56.2 56.0 81.4

81.3 54.2 57.2 80.6

77.2 61.1 60.0 82.2