At a local soda factory machines are programmed to fill each

At a local soda factory, machines are programmed to fill each can with exactly 12 oz. of soda. Every hour, a random sample of 5 cans is selected and the average volume is calculated. If the mean is significantly different than 12 oz, the machine is stopped and adjusted. One particular sample gave the following results:

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   12  
Ha:    u   =/   12  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    4          
tcrit =    +/-   2.776445105      
              
Getting the test statistic, as              
              
X = sample mean =    12.01          
uo = hypothesized mean =    12          
n = sample size =    5          
s = standard deviation =    0.029154759          
              
Thus, t = (X - uo) * sqrt(n) / s =    0.766964989          
              
As |t| < 2.776, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant deviation of the mean from 12 oz. The machine should not be adjusted. [CONCLUSION]