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 402.0 gram setting. It is believed that the machine is underfilling the bags. A 45 bag sample had a mean of 392.0 grams. A level of significance of 0.1 will be used. State the hypotheses. Assume the standard deviation is known to be 29.0. Enter the hypotheses:

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   402  
Ha:    u   <   402   [ANSWER, HYPOTHESES]

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Other info:
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.1   ,      
alpha =    0.1          
zcrit =    -   1.281551566      
              
Getting the test statistic, as              
              
X = sample mean =    392          
uo = hypothesized mean =    402          
n = sample size =    45          
s = standard deviation =    29          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.31317377          
              
Also, the p value is              
              
p =    0.010356544          
              
Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.