1 / 7

Understanding Confidence Intervals: Trade-offs in Precision and Reliability

This lab exercise focuses on confidence intervals (CIs), which are statistical tools used to estimate a population parameter based on sample data. The commonly used confidence level is 95%. The process for calculating a confidence interval for a population proportion includes determining the sample proportion, sample size, and standard deviation of the sampling distribution, followed by finding the critical value. An example illustrates how to calculate a CI for teenage TV viewing habits in Ohio, discussing the balance between confidence and precision required when constructing confidence intervals.

chaeli
Télécharger la présentation

Understanding Confidence Intervals: Trade-offs in Precision and Reliability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. STAT 135 LAB 12 Learning Objective: #77 TA: Dongmei Li

  2. Confidence Interval (CI) • A confidence interval is an interval calculated from sample data that will capture the true population parameter. • 95% is the most commonly used.

  3. How to find CI for p 1. Identify population proportion (p), sample proportion ( ) and sample size (n). 2. Calculate std. dev. of sampling distribution. => 3. Find the critical value z* from Table 21.1. 4. Calculate a Confidence interval. =>

  4. Example to find CI • Suppose I want to find the percentage of teenagers who watch TV more than 3 hours per day in Ohio. I did a survey in Ohio and found that 20 teenagers among those randomly selected 100 teenagers watch TV more than 3 hours per day. • Make a 95% Confidence interval for percentage of teenagers who watch TV more than 3 hours per day in Ohio.

  5. What CI means? • If we repeatedly take many samples and construct 95% CI for each sample. • Then the true proportion will be in 95% of the intervals.

  6. Confidence interval • There is a trade-off between confidence and precision. • You have to sacrifice precision if you want more confidence. • The higher confidence level (the more confident), the wider confidence interval (the less precise).

  7. Learning objective for Lab 12 • 77. There is a trade-off between confidence and reliability. In order to achieve a higher level of confidence, you must be willing to accept a larger margin of error (a wider interval) or pay the price of a larger sample size.

More Related