Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160 engines and the mean pressure was 7.9 lbs/square inch. Assume the variance is known to be 0.36. If the valve was designed to produce a mean pressure of 7.8 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve performs above the specifications?

State the null and alternative hypotheses for the above scenario.

Answer 1

Ho :   µ =   7.8                  
Ha :   µ >   7.8       (Right tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s =    0.6000                  
Sample Size ,   n =    160                  
Sample Mean,    x̅ =   7.9000                  
                          
degree of freedom=   DF=n-1=   159                  
                          
Standard Error , SE = s/√n =   0.6000   / √    160   =   0.0474      
t-test statistic= (x̅ - µ )/SE = (   7.900   -   7.8   ) /    0.0474   =   2.11
                          
critical t value, t* =        2.3500   [Excel formula =t.inv(α/no. of tails,df) ]              
                          
p-Value   =   0.0183   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis                       

Conclusion: There is not enough evidence to prove that the valve performs above the specifications.

Please revert in case of any doubt.

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