Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100 engines and the mean pressure was 4.9 lbs/square inch. Assume the standard deviation is known to be 0.6. If the valve was designed to produce a mean pressure of 4.8 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.

Answer 1

Ho :   µ =   4.8                  
Ha :   µ ╪   4.8       (Two tail test)          
                          
Level of Significance ,    α =    0.02                  
population std dev ,    σ =    0.6000                  
Sample Size ,   n =    100                  
Sample Mean,    x̅ =   4.9000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   0.6000   / √    100   =   0.0600      
Z-test statistic= (x̅ - µ )/SE = (   4.900   -   4.8   ) /    0.060   =   1.6667
                          

  
p-Value   =   0.0956    [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value>α, Do not reject null hypothesis                       
Conclusion: There is not enough evidence to conclude that valve does not perform to the specifications