The burning rate of a rocket propellant is being studied By

The burning rate of a rocket propellant is being studied. By government standards, the burning rate must be forty inches per minute. Also, it is well-known that the variance of the burning rate is four. From a random sample of size twenty-five, the mean burning rate is found to be forty-two. Test at the ninety-five percent confidence level to see if the observed mean burning rate meets government standards.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   40  
Ha:    u   =/   40  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    24          
tcrit =    +/-   2.063898562      
              
Getting the test statistic, as              
              
X = sample mean =    42          
uo = hypothesized mean =    40          
n = sample size =    25          
s = standard deviation = sqrt(4) =   2          
              
Thus, t = (X - uo) * sqrt(n) / s =    5          
              
Also, the p value is              
              
p =    4.15686E*10^-5          
              
As |t| > 2.064, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the observed mean burning rate DOES NOT meet government standards. [CONCLUSION]