Question

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*

denote the sample average braking distance for a random sample of 36 observations. Which values of

*x*

are more contradictory to *H*_{0} 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.)

You may need to use the appropriate table in the Appendix of Tables
to answer this question.

Answer #1

b)

population mean μ= | 120 |

sample mean 'x̄= | 117.200 |

sample size n= | 36.00 |

std deviation σ= | 11.000 |

std error ='σx=σ/√n= | 1.8333 |

test stat z = '(x̄-μ)*√n/σ= | -1.53 |

p value
= |
0.0630 |

since p value <0.10 ;

The new design does have a mean breaking distance less than 120 feet at 40 mph.

c)

P(Type II error) =P(Xbar>117.2|μ=115)=P(Z>(117.2-115)/1.833)=P(Z>1.2)= |
0.1151 |

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

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...

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...

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