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 o = 11. Let X denote the sample average braking distance for a random sample of 36 observations. Which values of x are more contradictory to He than 117.2? o s 117.2 OX 117.2 What is the p-value in this case? (Round your answer to four decimal places.) 0.0633 What conclusion is appropriate if a = 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.) 0.1151 x You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

Given that,
population mean(u)=120
standard deviation, σ =11
sample mean, x =117.2
number (n)=36
null, Ho: μ=120
alternate, H1: μ<120
level of significance, α = 0.1
from standard normal table,left tailed z α/2 =1.282
since our test is left-tailed
reject Ho, if zo < -1.282
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 117.2-120/(11/sqrt(36)
zo = -1.527
| zo | = 1.527
critical value
the value of |z α| at los 10% is 1.282
we got |zo| =1.527 & | z α | = 1.282
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : left tail - ha : ( p < -1.527 ) = 0.0633
hence value of p0.1 > 0.063, here we reject Ho
ANSWERS
---------------
b.
null, Ho: μ=120
alternate, H1: μ<120
test statistic: -1.527
critical value: -1.282
decision: reject Ho
p-value: 0.0633
we have enough evidence to support the claim that the new design does have a mean breaking
distance is less than 120 feet at 40mph
c.
Given that,
population mean(u)=120
standard deviation, σ =11
sample mean, x =115
number (n)=36
null, Ho: μ=120
alternate, H1: μ<120
level of significance, α = 0.1
from standard normal table,left tailed z α/2 =1.282
since our test is left-tailed
reject Ho, if zo < -1.282
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 115-120/(11/sqrt(36)
zo = -2.727
| zo | = 2.727
critical value
the value of |z α| at los 10% is 1.282
we got |zo| =2.727 & | z α | = 1.282
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : left tail - ha : ( p < -2.727 ) = 0.003
hence value of p0.1 > 0.003, here we reject Ho
ANSWERS
---------------
null, Ho: μ=120
alternate, H1: μ<120
test statistic: -2.727
critical value: -1.282
decision: reject Ho
p-value: 0.003
we have enough evidence to support the claim that the new design does have a mean breaking
distance is less than 120 feet at 40mph

Answer:
probability value = 0.0030
when true mean breaking distance is 115