Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 4.8 pounds/square inch (psi). Assume the population variance is 0.49. If the valve was designed to produce a mean pressure of 4.7 psi, is there sufficient evidence at the 0.02 level that the valve performs above the specifications?

Find the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Null hypothesis      

   
          
Alternative hypothesis       

  
          
We have given,          
Population mean for given example =4.7  
Sample mean=4.8  
Population standard deviation =   0.7  
Sample size for given example =   280  
Level of significance =   0.02  
Z test statistic formula


=2.39  

P value =0.0084.....................by using Z table or by using Excel command =1-NORMSDIST(2.39)