Question

A machine that is programmed to package 3.60 pounds of cereal is being tested for its accuracy. In a sample of 81 cereal boxes, the sample mean filling weight is calculated as 3.68 pounds. The population standard deviation is known to be 0.08 pound. [You may find it useful to reference the z table.] a-1. Identify the relevant parameter of interest for these quantitative data. Which one? The parameter of interest is the proportion filling weight of all cereal packages. The parameter of interest is the average 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? Yes, since the confidence interval does not contain the target filling weight of 3.60. No, since the confidence interval does not contain the target filling weight of 3.60. Yes, since the confidence interval contains the target filling weight of 3.60. No, since the confidence interval contains the target filling weight of 3.60. 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.)

          A machine that is programmed to package 3.60 pounds of
cereal is being tested for its accuracy. In a sample of 81 cereal
boxes, the sample mean filling weight is calculated as 3.68 pounds.
The population standard deviation is known to be 0.08
pound. [You may find it useful to reference the z
table.]
a-1. Identify the relevant parameter of
interest for these quantitative data.
Which one?
The parameter of interest is the proportion filling weight of
all cereal packages.
The parameter of interest is the average 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?
Yes, since the confidence interval does not contain the target
filling weight of 3.60.
No, since the confidence interval does not contain the target
filling weight of 3.60.
Yes, since the confidence interval contains the target filling
weight of 3.60.
No, since the confidence interval contains the target filling
weight of 3.60.
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.)

Added by Kimberly L.

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