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

The mean emission of all engines of a new design needs to be below 20 ppm if the design to meet new emission requirements. Ten engines are manufactured for testing purposes, and the mission level of each is determined. the emission data is: Based on the student\'s t-distribution. does the data supply sufficient evidence to conclude that this type of engine meets the new standard? Equations and others:

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]