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 The parameter of interest is the average filling weight of all cereal packages. 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.)
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.
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No, since the confidence interval contains the target filling weight of 6.60.
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Yes, since the confidence interval contains the target filling weight of 6.60.
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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.)
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