Question

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.95.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 110110 engines and the mean pressure was 6.06.0 pounds/square inch. Assume the variance is known to be 0.360.36. A level of significance of 0.10.1 will be used. Determine the decision rule.

Enter the decision rule.

Answer 1

Given that,
population mean(u)=5.9
standard deviation, σ = sqrt(0.36) = 0.6
sample mean, x =6
number (n)=110
null, Ho: μ=5.9
alternate, H1: μ>5.9
level of significance, alpha = 0.1
from standard normal table,right tailed z alpha/2 =1.282
since our test is right-tailed
reject Ho, if zo > 1.282
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 6-5.9/(0.6/sqrt(110)
zo = 1.748
| zo | = 1.748
critical value
the value of |z alpha| at los 10% is 1.282
we got |zo| =1.748 & | z alpha | = 1.282
make decision
hence value of | zo | > | z alpha| and here we reject Ho
p-value : right tail - ha : ( p > 1.748 ) = 0.0402
hence value of p0.1 > 0.0402, here we reject Ho
----------------------------------------------------------------------------------------
null, Ho: μ=5.9
alternate, the valve performs above the specifications, H1: μ>5.9
test statistic: 1.748
critical value: 1.282
decision: reject Ho
p-value: 0.0402, evidence to support that the valve performs above the specifications