The probability of a type II error for the t test for H0 : β1 = β10 can be computed in t...

The probability of a type II error for the t test for H₀ : β₁ = β₁₀ can be computed in the same manner as it was computed for the t tests of Chapter 8. If the alternative value of β₁ is denoted by β₁’, the value of

is first calculated, then the appropriate set of curves in Appendix Table A.17 is entered on the horizontal axis at the value of d, and b is read from the curve for n – 2 df. An article in the Journal of Public Health Engineering reports the results of a regression analysis based on n = 15 observations in which x = filter application temperature (?C) and y = % efficiency of BOD removal. Calculated quantities include , and . Consider testing at level .01 H₀ : β₁ = 1, which states that the expected increase in % BOD removal is 1 when filter application temperature increases by 1°C, against the alternative H_a : β₁ > 1 . Determine P(type II error) when .