An engineer has designed a valve that will regulate water pressure on an automob

Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 130 engines and the mean pressure was 4.3 lbs/square inch. Assume the standard deviation is known to be 0.6. If the valve was designed to produce a mean pressure of 4.4 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications? Step 1. State the hypotheses: H_0: H_a: Step 2. Find the value of the test statistic. Step 3. Specify if the test is one-tailed or two-tailed. A) One-Tailed Test B) Two-Tailed Test Step 4. Determine the conclusion. A) Reject Null Hypothesis B) Fail to Reject Null Hypothesis

Explanation / Answer

Given that,
population mean(u)=4.3
standard deviation, s =0.6
sample mean, x =4.4
number (n)=130
null, Ho: µ=4.3
alternate, H1: µ!=4.3
level of significance, a = 0.01
from standard normal table, two tailed z a/2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 4.4-4.3/(0.6/sqrt(130)
zo = 1.90029
| zo | = 1.90029
critical value
the value of |z a| at los 1% is 2.576
we got |zo| =1.90029 & | z a | = 2.576
make decision
hence value of |zo | < | z a | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.90029 ) = 0.05739
hence value of p0.01 < 0.05739, here we do not reject Ho

ANSWERS
---------------
1.
null, Ho: µ=4.3
alternate, H1: µ!=4.3
2.
test statistic: 1.90029
critical value: -2.576 , 2.576
decision: do not reject Ho
p-value: 0.05739

3.two tailed test
4. Fail to reject the null hypothesis

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