A machine that is programmed to package 3.90 pounds of cereal isbeing tested for its accuracy. In a sample of 64 cereal boxes, thesample mean filling weight is calculated as 3.95 pounds. Thepopulation standard deviation is known to be 0.14 pound. [You mayfind it useful to reference the z table.]
a-1. Identify the relevant parameter of interest for thesequantitative data.
The parameter of interest is the average filling weight of allcereal packages.
The parameter of interest is the proportion filling weight of allcereal packages.
a-2. Compute its point estimate as well as the margin of errorwith 90% confidence. (Round intermediate calculations to at least 4decimal places. Round "z" value to 3 decimal places and finalanswers to 2 decimal places.)
b-1. Calculate the 90% confidence interval. (Use rounded marginof error. Round your final answers to 2 decimal places.)
b-2. Can we conclude that the packaging machine is operatingimproperly?
No, since the confidence interval contains the target fillingweight of 3.90.
No, since the confidence interval does not contain the targetfilling weight of 3.90.
Yes, since the confidence interval contains the target fillingweight of 3.90.
Yes, since the confidence interval does not contain the targetfilling weight of 3.90.
c. How large a sample must we take if we want the margin oferror to be at most 0.02 pound with 90% confidence? (Roundintermediate calculations to at least 4 decimal places. Round "z"value to 3 decimal places and round up your final answer to thenext whole number.)
