Question

1. A new design for the braking system for a car has been proposed. For the current braking system, the true average braking distance at 40 mph under specified condition is known to be 120 ft.

It is proposed that the new braking system design will not be implemented if evidence from sample data indicates that the braking distance is HIGHER (compared to the current system).

(a) Let µ denote the true average braking distance. State an appropriate hypothesis test that would be useful in determining whether to implement the new braking system. (10 points)

(b) Test your hypothesis in question (a) using critical value approach.

Consider that Type I error α = 0.05, sample size n= 15, and X ¯= 122.5, and sample standard deviation s= 10. (20 points)

(c) Test your hypothesis in question (a) using p-value approach, with same information in question (b). (20 points)

2. A study to assess the capability of subsurface flow wetland systems to remove biochemical oxygen demand (BOD) and various other chemical constituents resulted in the accompanying data.

Here, x=BOD mass loading (kg/ha/d) and y=BOD mass removal (kg/ha/d)

x | 24 | 26 | 29 | 32 | 36 | 40 |

y | 32 | 40 | 39 | 46 | 50 | 60 |

(a) obtain the estimated β ^ 0 and β ^ 1coefficients, and write the linear regression equation. Show your work in excel file. (20 points)

(b) calculate SSE, SST and the coefficient of determination R 2. (20 points)

Answer #1

A new design for the braking system for a car has been proposed.
For the current braking system, the true
average
braking distance at 40 mph under specified condition is known to be
120 ft.
It is
proposed that the new braking system design will not be
implemented if evidence from sample data
indicates
that the braking distance is
HIGHER (compared to the current system).
Let µ denote the true average braking distance.
State an
appropriate hypothesis test that would...

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.
Let μ = true average braking distance for the new design at 40
mph. The hypotheses are:...

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 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...

b) Medical research has shown that repeated wrist extension
beyond 18 degrees increases the risk of wrist and hand injures. 40
students atschool used a proposed new mouse design, and while using
the mouse their wrist extensions were recorded for each one. The
mean wrist extension for theses 40 students was 20 with a sample
standard deviation of 3. i. (2 points) To test the hypothesis that
the mean wrist extension for people using this new mouse design
exceeds 18...

3. A store is trying out a new self-checkout system. They have
had complaints from customers about errors in pricing in the new
system, so the store runs a sample check. Out of 800 scanned items,
they identify 24 items that had the wrong price entered through the
self-checkout system.
(a) What is the estimate of the population proportion of errors
in the new self check-out system? (2 points)
(b) Their old system had an error rate of 0.04 or...

Question 5. (Two Variances)A new fuel injection system has been
engineered for pickup trucks. The new system and the old system
both produce about the same average miles per gallon. However,
engineers question which system (old or new) will give better
consistency in fuel consumption (miles per gallon) under a variety
of driving conditions. A random sample of 31 trucks were fitted
with the new fuel injection system and driven under different
conditions. For these trucks, the sample variance of...

A new extrasolar planet (outside our solar system) has been
discovered. This planet orbits a star of mass 1.05×1031 kg with a
period of 6.52 years . It is also known that the planet has an
eccentricity of 0.674.
Part A: What is the average velocity of the planet in its orbit?
in m/s
Part B: What is the distance of closest approach to its parent
start (perihelion)? d.perihelion in m
Part C: What is the farthest distance the planet...

A new fuel injection system has been engineered for pickup
trucks. The new system and the old system both produce about the
same average miles per gallon. However, engineers question which
system (old or new) will give better consistency in fuel
consumption (miles per gallon) under a variety of driving
conditions. A random sample of 41 trucks were fitted with the new
fuel injection system and driven under different conditions. For
these trucks, the sample variance of gasoline consumption was...

A new fuel injection system has been engineered for pickup
trucks. The new system and the old system both produce about the
same average miles per gallon. However, engineers question which
system (old or new) will give better consistency in fuel
consumption (miles per gallon) under a variety of driving
conditions. A random sample of 41 trucks were fitted with the new
fuel injection system and driven under different conditions. For
these trucks, the sample variance of gasoline consumption was...

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