A machine that is programmed to package 6.60 pounds of cereal is being tested for its accuracy. In a sample of 100 cereal boxes, the sample mean filling weight is calculated as 6.65 pounds. The...

A machine that is programmed to package 6.60 pounds of cereal is being tested for its accuracy. In a sample of 100 cereal boxes, the sample mean filling weight is calculated as 6.65 pounds. The population standard deviation is known to be 0.09 pound.[You may find it useful to reference the z table.]

a-1. Identify the relevant parameter of interest for these quantitative data.

multiple choice 1

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  The parameter of interest is the average filling weight of all cereal packages.

  
  
  
  


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  The parameter of interest is the proportion filling weight of all cereal packages.

  
  
  
  

a-2. Compute its point estimate as well as the margin of error with 95% confidence.(Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

b-1. Calculate the 95% confidence interval.(Use rounded margin of error. Round your final answers to 2 decimal places.)

b-2. Can we conclude that the packaging machine is operating improperly?

multiple choice 2

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  Yes, since the confidence interval does not contain the target filling weight of 6.60.

  
  
  
  


• 
  
  
  

  No, since the confidence interval contains the target filling weight of 6.60.

  
  
  
  


• 
  
  
  

  Yes, since the confidence interval contains the target filling weight of 6.60.

  
  
  
  


• 
  
  
  

  No, since the confidence interval does not contain the target filling weight of 6.60.

  
  
  
  

c. How large a sample must we take if we want the margin of error to be at most 0.01 pound with 95% confidence?(Round intermediate calculations to
at least
 4 decimal places. Round "z" value to 3 decimal places and round up your final answer to the next whole number.)