Question

here are summary statistics for the weights of pepsi in randomly selected cans: n = 36, \\( \bar { x } = 0.82414 \\) lb, s = 0.00572 lb. use a confidence level of 90% to complete parts (a) and (b) below.

a. there is a 90% 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.
b. approximately 90% of sample mean weights of pepsi in a can will fall between the lower bound and the upper bound.
c. one has 90% confidence that the sample mean weight of pepsi in a can is equal to the population mean weight of pepsi in a can.
d. one has 90% 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:

A confidence interval does not mean there is a certain probability that the population mean is in the interval (as in option A). It also does not refer to sample means (option B is wrong). Option C is incorrect as the sample mean is an estimate, not equal to the population mean. A 90% confidence interval means we are 90% confident that the interval contains the true population mean.

Answer:

D. One has 90% 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.