Question

a company fills boxes with approximately 23 pounds of oranges. to test the accuracy of the filling process, 344 boxes of oranges were selected at random and weighed. based on the sample, it is estimated that the average weight of all boxes of oranges filled by the company in an 8 - hour period is 23.1 pounds, with an associated margin of error of 0.19 pounds. which of the following is the best interpretation of this estimate?
a. plausible values for the average weight of all boxes of oranges filled by the company are between 22.91 pounds and 23.29 pounds.

b. plausible values for the average weight of all boxes of oranges filled by the company are less than 22.91 pounds or greater than 23.29 pounds.

c. the average weight of all boxes of oranges filled by the company is less than 23.01 pounds.

d. the average weight of all boxes of oranges filled by the company is greater than 23.01 pounds.

Explanation:

To interpret the estimate, we use the formula for a confidence interval: \(\text{Estimate} \pm \text{Margin of Error}\). Here, the estimate (sample mean) is \(23.1\) pounds and the margin of error is \(0.19\) pounds.

Calculating the lower bound: \(23.1 - 0.19 = 22.91\) pounds.
Calculating the upper bound: \(23.1 + 0.19 = 23.29\) pounds.

This means the plausible values for the population mean (average weight of all boxes) lie between the lower and upper bounds. Option A states this correctly. Option B is incorrect as it describes values outside the interval. Options C and D make incorrect claims about the population mean being less than or greater than a value, which isn’t supported by the interval.

Answer:

A. Plausible values for the average weight of all boxes of oranges filled by the company are between 22.91 pounds and 23.29 pounds.