The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions ("Experimental Measurement of the Stopping Performance of a Tractor-Semitrailer from Multiple Speeds," NHTSA, DOT HS 811 488, June 2011):
32.1 30.6 31.4 30.4 31.0 31.9
The cited report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed.
a. Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using α = .01.
b. Determine the probability of a type II error when α = .01, σ = .65, and the actual value of μ is 31. Repeat this for μ = 32 (use either statistical software or Table A.17).
c. Repeat (b) using σ = .80 and compare to the results of (b).
d. What sample size would be necessary to have α = .01 and β = .10 when μ = 31 and σ = .65?