The mean emission of all engines of a new design needs to he

The mean emission of all engines of a new design needs to he below 20 ppm it the design i to meet new emission requirements, fen engines are manufactured for testing purposes, and the mission level of each is determined. 1 he emission data is: Based on the student\'s docs the data supply sufficient evidence to this type of engine meets the new standard?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   20  
Ha:    u   <   20  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    9          
tcrit =    -2.306 [as in your table]      
              
Getting the test statistic, as              
              
X = sample mean =    17.17          
uo = hypothesized mean =    20          
n = sample size =    10          
s = standard deviation =    2.981442604          
              
Thus, t = (X - uo) * sqrt(n) / s =    -3.001649526          
              
As t < -2.306, we   REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the mean emission is below 20ppm and it satisifes the new emission requirements. [CONCLUSION]