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
Ha: μ > 120
H0: p̂ = 120
Ha: p̂ <
120
H0: μ = 120
Ha: μ ≠ 120
H0: μ = 120
Ha: μ < 120
H0: p̂ = 120
Ha: 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).
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 (a) Define the parameter of interest. O p-true proportion of cars whose braking distances reduced μ-true average...
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 o = 11. Let X...
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...
A new design for the braking system of a car has been proposed. For the current system, the true average braking distance at 40 mph is known to be 120ft. 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 new design for the braking system of a car has been proposed. For the current system, the true average braking distance at 40...
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) What is the P-value in this case? (Round your answer to four decimal places.) ...... (c)...
A new design for the breaking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40mph 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. State the relevant hypothesis, and describe the type I and type II errors in the context of this...
It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 37 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 111 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the...
It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 122 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 33 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 115 feet. Assume that the population standard deviation is 24 feet. a. State the null and the alternative hypotheses...
It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 32 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 115 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the...
It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 35 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 113 feet. Assume that the population standard deviation is 22 feet. (You may find it useful to reference the...