Question

A biotech company produces a therapeutic drug whose concentration has a standard deviation of 0.2 g/l(gram per liter). A new method of producing this drug has been proposed, although some additional cost is involved. Management will authorize a change in production technique only if the standard deviation of the concentration in the new process is less than 0.2 g/l. With the data of sample size n = 10 in the table below, conduct a hypothesis testing analysis to determine whether this new process can be implemented.

16.628 16.622 16.627 16.623 16.618 16.630 16.631 16.624 16.622 16.626 (unit: g/l)

Answer 1

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   0.0040
Ho :   σ =   0.2
Ha :   σ <   0.2
      
Level of Significance ,    α =    0.05
sample Std dev ,    s =    0.004040077
Sample Size ,   n =    10
      
Chi-Square Statistic   X² = (n-1)s²/σ² =    0.004
      
degree of freedom,   DF=n-1 =    9
      
one tail test       
lower critical value   =   3.325112843
p-value   =   0.00000

P value < alpha , Reject the null hypothesis      

There is sufficient evidence that standard deviation of the concentration in the new process is less than 0.2 g/l

and this new process can be implemented.

Thanks in advance!

revert back for doubt

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