As a commercial buyer for a private supermarket brand, suppose you take a random sample of 12 cans of beans packed at a canning plant. The mean weight per can is found out to be 15.97oz with standard deviation of 0.15oz.
Assume that net weights per can are normally distributed.
Q. What is the 95% confidence interval for the mean weight per can?
Q. If the answer to the previous question were (15.85, 16.09), which of the following would be a correct interpretation of the interval?
I. The weight of at least 95% of the cans made by this company will be greater than 15.85oz.
II. We are 95% confident that the mean weight of all cans made by this company will be less than 16.05oz.
III. The probability that the mean weight of all cans is between 15.85oz and 16.09oz is 0.95.