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 μ = true average braking distance for the old design O p = true proportion of cars whose braking distances did not reduce O p = true proportion of cars whose braking distances reduced State the relevant hypotheses. ⒸHO: #= 120 Ha: > 120 OH: P = 120 H₂: P = 120 ⒸHo: p = 120 Ha: p < 120 Ho: = 120 H: 120 Ho: M = 120 H₂: M = 120 (b) Suppose braking distance for the new system is normally distributed with a = 11. 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? x≤ 117.2 Ox≥ 117.2 What is the P-value in this case? (Round your answer to four decimal places.) 0.093 x What conclusion is appropriate if a = 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.
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 μ = true average braking distance for the old design O p = true proportion of cars whose braking distances did not reduce O p = true proportion of cars whose braking distances reduced State the relevant hypotheses. ⒸHO: #= 120 Ha: > 120 OH: P = 120 H₂: P = 120 ⒸHo: p = 120 Ha: p < 120 Ho: = 120 H: 120 Ho: M = 120 H₂: M = 120 (b) Suppose braking distance for the new system is normally distributed with a = 11. 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? x≤ 117.2 Ox≥ 117.2 What is the P-value in this case? (Round your answer to four decimal places.) 0.093 x What conclusion is appropriate if a = 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.
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Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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Transcribed Image Text:(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 μ = true average braking distance for the old design
Op = true proportion of cars whose braking distances did not reduce
Op = true proportion of cars whose braking distances reduced
State the relevant hypotheses.
O Ho: 120
H₂: > 120
ⒸHO: P = 120
H₂: P = 120
ⒸH₂: p = 120
Ha: p < 120
Ho: = 120
Ha: # < 120
ⒸH₂ = 120
H₂H 120
(b) Suppose braking distance for the new system is normally distributed with = 11. 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?
Ⓒx≤ 117.2
Oxz1172
What is the P-value in this case? (Round your answer to four decimal places.)
0.093
x
What conclusion is appropriate if a = 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.
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