The U.S. Post Office is interested in estimating the mean weight of packages shipped using the overnight service. They plan to sample 300 packages. A pilot sample taken last year showed that the standard deviation in weight was about 0.15 pound. If they are interested in an estimate that has 95 percent confidence, what margin of error can they expect?

Question

BlackTom AI · Accepted Answer

To assess the margin of error for a 95% confidence interval when estimating a mean, we use the formula E = z_{alpha/2} * sigma / sqrt(n).

Option 1: About 0.0003 pound. This is far smaller than the calculation would yield. Using sigma = 0.15, n = 300, sqrt(n) ≈ 17.32, and z_{0.025} = 1.96, the margin of error would be 1.96 * 0.15 / 17.32 ≈ 0.01698, not 0.0003. So this choice underestimates the true spread dramatically.

Option 2: Approximately 0.017 pound. This aligns with the standard margin-of-error computation: E = 1.96 * 0.15 / sqrt(300) ≈ 0.01698 ≈ 0.017. The numbers fit the given 95% confidence level and sample size.

Option 3: About 1.96. This value is the z-score for 95% confidence, not the margin of error itself. The margin of error scales with sigma and n, not directly to the z-score in pounds.

Option 4: Can't be determined without knowing the population mean. Not necessary here. For margins of error in confidence intervals, we use the standard deviation (sigma) and the sample size; the population mean is not required to compute E.

OSC 2030-009 Fall 2025 SUBMIT: Graded Homework Module 7 (Chap 8)

View Explanation

Log in for full answers

Similar Questions

位置5的问题 As the sample size increases, the margin of error decreases.TrueFalse

位置4的问题 If the margin of error in an interval estimate of μ is 3.8, the interval estimate equals 1.9 (that is half of 3.8).TrueFalse

A 96 % confidence interval for a mean was constructed. The confidence interval is as follows 6.1 ± 3.5 . What is the margin of error? Recall: a confidence interval is computed using 𝑥 ¯ ± 𝐸 . c07.p061.q025

What is the margin of error? Remember to use the same standard error you calculated in Question 7.24.

What is the margin of error?

A hospital emergency room (ER) has collected a sample of n = 40 to estimate the mean wait time in the ER. It has found the population standard deviation is 32. Using a 90 percent confidence level, what is its margin of error?

More Practical Tools for International Students

Exam Browser Assistant

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler