A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 420.0 gram setting. It is believed that the machine is underfilling the bags. A 33 bag sample had a mean of 417.0 grams. A level of significance of 0.01 will be used. Determine the decision rule. Assume the variance is known to be 576.00.

Answer

The decision rule is

Fail to reject the null hypothesis

The conclusion is  

There is no sufficient evidence to conclude that the machine is underfilling the bags

Step-by-step-explanation:

From the question we are told that

   The  population mean is  

    The  sample size is  n  =  33 bags

    The sample mean is  

     The level of significance is  

     The  variance  is  

The  null hypothesis is

The alternative hypothesis is

Generally the standard deviation is mathematically represented as

=>    

=>    

Generally the test statistics is mathematically represented as

=>    

=>      

From the z table  the area under the normal curve to the left corresponding to    -0.71807   is  

Generally looking at the values we see that

              ,  hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is  

There is no sufficient evidence to conclude that the machine is underfilling the bags

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step-by-step explanation:

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step-by-step explanation: