The Number of Miles Useful Tread Wear (In 1000's) Was $H _ { 0 } : \alpha _ { 1 } = \alpha _ { 2 } = \alpha _ { 3 } = \alpha _ { 4 } = \alpha _ { 5 } = 0$

Essay

The number of miles useful tread wear (in 1000's) was determined for tires of five different makes of subcompact car (factor A, with I = 5) in combination with each of four different brands of radial tires (factor B, with J = 4), resulting in IJ = 20 observations. The values SSA = 30, SSB = 45, and SSE = 60 were then computed. Assume that an additive model is appropriate.
a. Test $H _ { 0 } : \alpha _ { 1 } = \alpha _ { 2 } = \alpha _ { 3 } = \alpha _ { 4 } = \alpha _ { 5 } = 0$
(no differences in true average tire lifetime due to makes of cars) versus $H _ { a } : \text { at least one } \alpha _ { i } \neq 0$
using a level .05 test.
b. $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = 0$
(no differences in "true" average tire lifetime due to brands of tires) versus $H _ { a } : \text { at least one } \beta _ { \mathrm { j } } \neq 0$
using a level .05 test.