A manufacturer of potato chips would like t know whether its bag filling machine

Question

A manufacturer of potato chips would like t know whether its bag filling machine works correctly at the 421 gram setting. IT is believed that the machine is overfilling the bags. A 44 bag sample had a mean of 431 grams. Assume a population standard deviation of 26. Is there sufficient evidence at the 0.1 level that the bags are overfilled? Find the value of the z test statistic (Round your answer to 2 decimal places.) Specify if the test is one - tailed or two - tailed One -Tailed Test Two - Tailed Test Find the P - value of the z test statistic (Round your answer to 4 decimal places.) Determine the value of the level of significance. Determine the conclusion. Reject Null Hypothesis Fail to Reject Null Hypothesis A newsletter publisher believes that over 69% of their readership own a Rolls Royce. Is there sufficient evidence at the 0.10 level to substantiate the publisher's claim? State the hypotheses:

Explanation / Answer

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   421  
Ha:    u   >   421   [ANSWER]

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2.

              
  
Getting the test statistic, as              
              
X = sample mean =    431          
uo = hypothesized mean =    421          
n = sample size =    44          
s = standard deviation =    26          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.551249839   [ANSWER]

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3.

As we can see, this is a    right   tailed test.  

Hence, it is ONE TAILED. [ANSWER]

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4.

Hence, the p value is              
              
p =    0.005366868   [ANSWER]

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5.      

As given,

alpha = 0.1 [ANSWER]

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6.

As P < 0.1, we REJECT THE NULL HYPOTHESIS.

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