Question

here are summary statistics for the weights of pepsi in randomly selected cans: ( n = 36 ), ( overline{x}=0.82409 \text{lb} ), ( s = 0.00569 \text{lb} ). use a confidence level of ( 90% ) to complete parts (a) through (d) below.
( 0.82249 \text{lb}<mu<0.82569 \text{lb} )
(round to five decimal places as needed.)
d. write a brief statement that interprets the confidence interval. choose the correct answer below
( \bigcirc ) a. 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.
( \bigcirc ) b. 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
( \bigcirc ) c. 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.
( \bigcirc ) d. approximately ( 90% ) of sample mean weights of pepsi in a can will fall between the lower bound and the upper bound.

Explanation:

A confidence interval gives a range of values within which we are confident the population parameter (here, the population mean weight of Pepsi in a can) lies. A 90% confidence level means that if we were to take many samples and construct confidence intervals in the same way, about 90% of those intervals would contain the true population mean.

• Option A is incorrect because the sample mean is just one estimate, and the confidence interval is about the population mean, not stating that the sample mean is equal to the population mean.
• Option B is correct. The interpretation of a confidence interval is that we have a certain level of confidence (90% in this case) that the interval contains the true population parameter (the population mean weight of Pepsi in a can).
• Option C is incorrect. It's not about a "chance" for a single - constructed interval. The confidence level refers to the long - run proportion of intervals (if we were to construct many) that contain the true value.
• Option D is incorrect. The confidence interval is about the population mean, not about the sample means.

Answer:

B. 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.