An engineer designed a vaive that will regulate water pressure on an automobile
ID: 3359843 • Letter: A
Question
An engineer designed a vaive that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.1 Ibs/square inch. It is believed that the valve performs above the specifications. The valve was tested on 26 engines and the mean pressure was 6.4 lbs/square inch with a standard deviation of 0.6. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places Answer How to enter your answer Tables Keypad , I1 Reject Ho if tExplanation / Answer
Given that,
population mean(u)=6.1
sample mean, x =6.4
standard deviation, s =0.6
number (n)=26
null, Ho: =6.1
alternate, H1: >6.1
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.708
since our test is right-tailed
reject Ho, if to > 1.708
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =6.4-6.1/(0.6/sqrt(26))
to =2.55
| to | =2.55
critical value
the value of |t | with n-1 = 25 d.f is 1.708
we got |to| =2.55 & | t | =1.708
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.5495 ) = 0.00865
hence value of p0.05 > 0.00865,here we reject Ho
ANSWERS
---------------
null, Ho: =6.1
alternate, H1: >6.1
test statistic: 2.55
critical value: 1.708
decision: reject Ho
p-value: 0.00865