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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 new design Op = true proportion of cars whose braking distances did not reduce Op = true proportion of cars whose braking distances reduced O μ = true average braking distance for the old design State the relevant hypotheses. O Ho: 120 H₂: μ = 120 O Ho: p= 120 H: <120 OHO: H = 120 H: > 120 (9) Αγώ με το 120 Hg: μ < 120 O Ho: $ = 120 H₂: p= 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? Ox2 117.2 xs 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.)

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 new design Op = true proportion of cars whose braking distances did not reduce Op = true proportion of cars whose braking distances reduced O μ = true average braking distance for the old design State the relevant hypotheses. O Ho: 120 H₂: μ = 120 O Ho: p= 120 H: <120 OHO: H = 120 H: > 120 (9) Αγώ με το 120 Hg: μ < 120 O Ho: $ = 120 H₂: p= 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? Ox2 117.2 xs 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.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 μ = true average braking distance for the new design O p = true proportion of cars whose braking distances did not reduce O p = true proportion of cars whose braking distances reduced O μ = true average braking distance for the old design State the relevant hypotheses. Ho: μ = 120 H₂: μ = 120 O Ho: p = 120 Ha: p < 120 O Ho: μ = 120 H₂: μ> 120 ⒸHo: μ = 120 H₂: μ< 120 O Ho: p = 120 H₂: p = 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? O x ≥ 117.2 O 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? O 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.)
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 μ = true average braking distance for the new design O p = true proportion of cars whose braking distances did not reduce O p = true proportion of cars whose braking distances reduced O μ = true average braking distance for the old design State the relevant hypotheses. Ho: μ = 120 H₂: μ = 120 O Ho: p = 120 Ha: p < 120 O Ho: μ = 120 H₂: μ> 120 ⒸHo: μ = 120 H₂: μ< 120 O Ho: p = 120 H₂: p = 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? O x ≥ 117.2 O 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? O 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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