Question

here are summary statistics for the weights of pepsi in randomly selected cans: n = 36, \\( \overline { x } = 0.82411 \mathrm { lb } \\), s = 0.00566 lb. use a confidence level of 99% to complete parts (a) through (d) below. (round to two decimal places as needed.) b. find the margin of error. e = 0.00257 lb (round to five decimal places as needed.) c. find the confidence interval estimate of \\( \mu \\). 0.82154 lb < \\( \mu \\) < 0.82668 lb (round to five decimal places as needed.) d. write a brief statement that interprets the confidence interval. choose the correct answer below. a. one has 99% confidence that the sample mean weight of pepsi in a can is equal to the population mean weight of pepsi in a can. b. there is a 99% chance that the true value of the population mean weight of pepsi in a can will fall between the lower bound and the upper bound. c. approximately 99% of sample mean weights of pepsi in a can will fall between the lower bound and the upper bound. d. one has 99% confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of pepsi in a can.

Explanation:

• Option A: Incorrect. The confidence interval is about the population mean, not stating the sample mean equals the population mean.
• Option B: Incorrect. It's not about a "chance" for the population mean to fall in the interval in a frequentist sense (confidence intervals are about the method's reliability, not a probability for a single interval).
• Option C: Incorrect. It's about the population mean, not sample means.
• Option D: Correct. A 99% confidence interval means we have 99% confidence that the interval (lower bound to upper bound) contains the true value of the population mean.

Answer:

D. One has 99% confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of Pepsi in a can.