Question

# A new design for the braking system on a certain type of car has been proposed....

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.

(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.)

You may need to use the appropriate table in the Appendix of Tables to answer this question.

b)

 population mean μ= 120 sample mean 'x̄= 117.2 sample size    n= 36 std deviation σ= 11 std error ='σx=σ/√n= 1.8333 test stat z = '(x̄-μ)*√n/σ= -1.53 p value        = 0.063

since p value <0.10 ;

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

c)

 P(Type II error) =P(Xbar>117.2|μ=115)=P(Z>(117.2-115)/1.833)=P(Z>1.2)= 0.1151

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