A manufacturer of banana chips would like to know whether it

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 419 gram setting. It is believed that the machine is under filling or overfilling the bags. A 47 bag sample had a mean of 417 grams. Assume a population variance of 729. Is there sufficient evidence at the 0.05 level of significance that the bags are under filled or overfilled? Specify the type of hypothesis test. A. Left-Tailed Test B. Right-Tailed Test C. Two-Tailed Test

Solution

A)

OPTION C: TWO TAILED TEST. [ANSWER]

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Formulating the null and alternative hypotheses,              
              
Ho:   u   =   419  
Ha:    u   =/   419  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha/2 =    0.025          
zcrit =    +/-   1.959963985      
              
Getting the test statistic, as              
              
X = sample mean =    417          
uo = hypothesized mean =    419          
n = sample size =    47          
s = standard deviation =    27          
              
Thus, z = (X - uo) * sqrt(n) / s =    -0.507826267          
              
Also, the p value is              
              
p =    0.611575187          
              
As P > 0.06, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

There is no significant evidence that the bags are under filled or overfilled at 0.05 level. [CONCLUSION]