Question

A machine that is programmed to package 5.20 pounds of cereal is being tested for its accuracy. In a sample of 100 cereal boxes, the sample mean filling weight is calculated as 5.26 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. Multiple choice, pick one answer.

-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.)

point estimate = ?

Margin or error = ?

b-1. Calculate the 95% confidence interval. (Use rounded margin of error. Round your final answers to 2 decimal places.)

Confidence interval = ?

b-2. Can we conclude that the packaging machine is operating improperly? Multiple choice, pick one.

-Yes, since the confidence interval contains the target filling weight of 5.20.

-No, since the confidence interval does not contain the target filling weight of 5.20.

-No, since the confidence interval contains the target filling weight of 5.20.

-Yes, since the confidence interval does not contain the target filling weight of 5.20.

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.)

Sample size = ?

Answer 1

The solution to this problem is given by