Question

A machine that is programmed to package 3.30 pounds of cereal is being tested for its accuracy. In a sample of 49 cereal boxes, the sample mean filling weight is calculated as 3.39 pounds. The population standard deviation is known to be 0.14 pound. [You may find it useful to reference the z table.]

a-1. Identify the relevant parameter of interest for these quantitative data.

• 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 99% 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 99% 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?

• No, since the confidence interval contains the target filling weight of 3.30.

• No, since the confidence interval does not contain the target filling weight of 3.30.

• Yes, since the confidence interval contains the target filling weight of 3.30.

• Yes, since the confidence interval does not contain the target filling weight of 3.30.

c. How large a sample must we take if we want the margin of error to be at most 0.03 pound with 99% 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.)

Answer 1