Question
upstudy study bank question image url

The closer the sample mean is to the population mean, the smaller the sampling error. the larger the sampling error. the sampling error equals 1. none of these alternatives is correct.

Ask by Moran Parry. in the United States
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The closer the sample mean is to the population mean, the smaller the sampling error.

Solution

1. The sampling error is defined as the difference between the sample mean and the population mean. Mathematically, if we let \( \bar{x} \) be the sample mean and \( \mu \) be the population mean, then the sampling error \( e \) is given by \[ e = \bar{x} - \mu \] 2. If \( \bar{x} \) is closer to \( \mu \), then the absolute difference \( |e| \) is smaller. This implies that the sampling error is smaller. 3. Therefore, the correct conclusion is: **The closer the sample mean is to the population mean, the smaller the sampling error.**

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

The Deep Dive

The closer the sample mean is to the population mean, the smaller the sampling error, which is essentially the difference between the two. It’s a fundamental concept in statistics that helps to ensure that our sample data is a good representation of the overall population, making our conclusions more reliable. In practice, reducing sampling error is crucial for researchers. Using larger samples tends to yield means that more accurately reflect the population mean. However, common mistakes include drawing conclusions from small or unrepresentative samples, which can greatly inflate sampling errors and lead to misguided insights. Always strive for quality samples!

Related Questions

Latest Statistics Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy