EXAMPLE 12.21

Testing the first contrast of interest. The sample contrast that estimates ψ₁ is

with standard error

= 0.1988

The t statistic for testing H₀₁: ψ₁ = 0 versus H_a1: ψ₁ > 0 is

Because s_p has 100 degrees of freedom, software using the t(100) distribution gives the two-sided P-value as P = 0.8341. If we used Table D, we would conclude that P > 2(0.25) = 0.50. The P-value is very large, so there is little evidence against H₀₁.