Question

A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design.

(a) Define the parameter of interest.

μ = true average braking distance for the old design

p̂ = true proportion of cars whose braking distances did not reduce    

p̂ = true proportion of cars whose braking distances reduced

μ = true average braking distance for the new design

State the relevant hypotheses.

H₀: μ = 120
H_a: μ > 120

H₀: p̂ = 120
H_a: p̂ < 120     

H₀: μ = 120
H_a: μ ≠ 120

H₀: μ = 120
H_a: μ < 120

H₀: p̂ = 120
H_a: p̂ ≠ 120

(b) Suppose braking distance for the new system is normally distributed with σ = 11. Let X denote the sample average braking distance for a random sample of 36 observations. Which values of x are more contradictory to H₀ than 117.2?

x ≤ 117.2

x ≥ 117.2   

What is the P-value in this case? (Round your answer to four decimal places.)

What conclusion is appropriate if α = 0.10?

The new design does have a mean breaking distance less than 120 feet at 40 mph.

The new design does not have a mean breaking distance less than 120 feet at 40 mph.   

(c) What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft and the test from part (b) is used? (Round your answer to four decimal places.)
  

Please show me how to work part (c). The answer is not .8849. It is supposed to be .0741 but I do not know how to get it.

Answer 1

Note: In part (c), it was asked the type II error probability.