A machine that is programmed to package 2.24 pounds of cereal is
being tested for its accuracy. In a sample of 9 cereal boxes, the
sample mean filling weight is calculated as 2.24 pounds. The
population standard deviation is known to be 0.12 pound. Use Table
1. 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 4 decimal
places. Round "z-value" to 3 decimal places and final answers to 2
decimal places.) Point estimate Margin of error b-1. Calculate the
95% confidence interval. (Use rounded margin of error. Round your
final answers to 2 decimal places.) Confidence interval to b-2. Can
we conclude that the packaging machine is operating improperly?
multiple choice 2 Yes, since the confidence interval contains the
target filling weight of 2.24. Yes, since the confidence
interval does not contain the target filling weight of 2.24. No,
since the confidence interval contains the target filling weight of
2.24. No, since the confidence interval does not contain the target
filling weight of 2.24. c. How large a sample must we take if we
want the margin of error to be at most 0.04 pound with 95%
confidence? (Round intermediate calculations to 4 decimal places.
Round "z-value" to 3 decimal places and round up your final answer
to the next whole number.) Sample size