Solved: The probability of a type II error for the t test
Chapter 12, Problem 43E(choose chapter or problem)
Problem 43E
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 Ha : β1 > 1 . Determine P(type II error) when .
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