A new process for synthesizing methanol from methane is under study to evaluate

Question

A new process for synthesizing methanol from methane is under study to evaluate its technical feasibility. Design simulations indicate that the reactor must have a mean mthane conversion greater thatn 40% for the process to be feasible. In an initial study, 42 runs were made. The average conversion was 44% and the standard deviation was 6%. If it can be concluded that the mean conversion is greater than 40%, further evaluation of the process will be concluded.

A. State the appropriate null and alternative hypotheses.

B. Find the test statistic value and give the P-value associated with the test in part (a).

C Should futher evaluation of the process be conducted? Explain.

D. What assumptions you made in part (b) regarding the methane conversion.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   40  
Ha:    u   >   40  

b)

              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    44          
uo = hypothesized mean =    40          
n = sample size =    42          
s = standard deviation =    6          
              
Thus, z = (X - uo) * sqrt(n) / s =    4.320493799 [TEST STATISTIC]          
              
Also, the p value is              
              
p =    7.78402E-06 [P VALUE]

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c)          
              
As P is very small, then YES, further evaluation should be conducted.

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d)

We have assumed that the sampling distribution of the mean average conversion is approximately normal.

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