位置1的问题 From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately 题库 1/1[input]. (Note: your answer should retain THREE decimal places.)

Question

BlackTom AI · Accepted Answer

We are given a population of size N = 500 with population variance σ^2 = 900, so the standard deviation is σ = sqrt(900) = 30. A sample of size n = 225 is drawn. The standard error of the mean depends on whether we apply the finite population correction (FPC).

First, without FPC (simple random sampling from an infinite population):
- Standard error (SE) = σ / sqrt(n) = 30 / sqrt(225) = 30 / 15 = 2.000.

Second, with finite population correction (appropriate for sampling without replacement from a finite population):
- FPC factor = sqrt((N - n) / (N - 1)) = sqrt((500 - 225) / (500 - 1)) = sqrt(275 / 499) ≈ sqrt(0.551102) ≈ 0.7424.
- Adjusted SE = (σ / sqrt(n)) * FPC = 2.000 * 0.7424 ≈ 1.4848.
- When rounded to three decimal places, this becomes 1.485.

A note on the given numeric result: if someone reports approximately 1.535, that would correspond to a slightly larger correction factor than the standard FPC here or a different interpretation of the sampling scheme. Using the conventional finite population correction for the given N and n yields about 1.485 to three decimals.

Summary of the key computations:
- σ = sqrt(900) = 30
- Without FPC: SE = 30 / sqrt(225) = 2.000
- With FPC: SE = 2.000 * sqrt((500 - 225) / (500 - 1)) ≈ 2.000 * 0.7424 ≈ 1.485

Since the answer options are not provided in the input, these steps show how to compute the standard error under both common interpretations and what the three-decimal result would be under the finite population correction.

位置1的问题 From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately 题库 1/1[input]. (Note: your answer should retain THREE decimal places.)

View Explanation

Log in for full answers

Similar Questions

A population has a mean of 37 and a standard deviation of 13. A sample of size 5 is taken at random from this population. The standard error of the sample mean equals (up to three decimal places):

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler