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 tru braking distance for the new design. (a) Define the parameter of interest. Op=true proportion of cars whose braking distances reduced - true average braking distance for the new design O=true average braking distance for the old design Op=true proportion of cars whose braking distances did not reduce State the relevant hypotheses. OH: P-120 M₂: P-120 OH:120 M₁R 120 OHP-120 H₂: <120 ⒸH₂-120 M₂: 120 ⒸH₂-120 M₂: 120 (b) Suppose braking distance for the new system is normally distributed with 13. Let X denote the sample average braking distance for a random sample of 36 observations. Which values of x are more contradictory to Ho than 117.2? 0x2 117.2 exs 117.2 What is the P-value in this case? (Round your answer to four decimal places.) What conclusion is appropriate if a 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.
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 tru braking distance for the new design. (a) Define the parameter of interest. Op=true proportion of cars whose braking distances reduced - true average braking distance for the new design O=true average braking distance for the old design Op=true proportion of cars whose braking distances did not reduce State the relevant hypotheses. OH: P-120 M₂: P-120 OH:120 M₁R 120 OHP-120 H₂: <120 ⒸH₂-120 M₂: 120 ⒸH₂-120 M₂: 120 (b) Suppose braking distance for the new system is normally distributed with 13. Let X denote the sample average braking distance for a random sample of 36 observations. Which values of x are more contradictory to Ho than 117.2? 0x2 117.2 exs 117.2 What is the P-value in this case? (Round your answer to four decimal places.) What conclusion is appropriate if a 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.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Transcribed Image Text: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.
O p = true proportion of cars whose braking distances reduced
Ⓒ μ = true average braking distance for the new design
O μ = true average braking distance for the old design
Op = true proportion of cars whose braking distances did not reduce
State the relevant hypotheses.
O Ho: p = 120
H₂: p * 120
O Ho: μ = 120
H₂:μ* 120
O Ho: P = 120
H₂: P < 120
ⒸHo: μ = 120
H₂: μ< 120
O Ho: μ = 120
H₂: > 120
(b) Suppose braking distance for the new system is normally distributed with = 13. Let X denote the sample average braking distance for a random sample of 36 observations. Which values of x are more contradictory to H. than 117.2?
O x 2 117.2
Ox≤ 117.2
What is the P-value in this case? (Round your answer to four decimal places.)
What conclusion is appropriate if a = 0.10?
The new design does have a mean breaking distance less than 120 feet at 40 mph.
O 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.)
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