A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pound.
a. Identify the relevant parameter of interest for these quantitative data and compute its point estimate as well as the margin of error with 95% confidence.
b. Can we conclude that the packaging machine is operating improperly?
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?