# **Simulating Confidence Intervals

This applet generates confidence intervals for means or proportions. The options for confidence intervals for means include "z with sigma," "z with s," or "t." The options for confidence intervals for proportions are "Wald," "Adjusted Wald," or "Score." Users set the population parameters, sample size, number of intervals, and confidence level. Click "Sample," and the applet will graph the intervals. Intervals shown in green contain the true population mean or proportion, while intervals in red do not. The true mean or proportion is shown by a blue line. The applet displays the proportion of intervals containing the population parameter for each sample and a running total of all the samples. Users can also click on a particular interval to display the numerical interval or sort the displayed confidence intervals from smallest to largest. This applet is part of a collection designed to accompany the textbook "Investigating Statistical Concepts, Applications, and Methods" (ISCAM) and is used in Exploration 4.3 on page 327, Investigation 4.3.6 on page 331, and Exploration 4.4 on page 350. This applet also supplements "Workshop Statistics: Discovery with Data," 2nd edition, Activity 19-5 on page 403. Additional materials written for use with these applets can be found at http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/rowell/final/16_cireview_bc322_2.doc and http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/rowell/final/15_sampdistreview_bc322_1.doc.
Rating:
Author Name:
Allan Rossman, Beth Chance
Technical Requirements:
Java Applet
Content Quality Concerns:
The terms "Wald" and "adjusted Wald" might be unfamiliar to students and some instructors, and the only explanation of these terms in relation to the applet is in the textbook. If "t" is selected for confidence intervals for means, the sigma box does not change to s. There is nothing to keep students from generating intervals when conditions are not satisfied (e.g., p = 0.05, n = 20). There are no instructions on how to use the applet within the web page itself, for those who do not have the accompanying activity workbook.
Content Quality Strengths:
This applet provides an excellent, accurately displayed visual presentation of confidence intervals which can help students understand the meaning of confidence. The applet generates several types of confidence intervals, such as Wald, adjusted Wald, or score for proportions and z or t for means. The ability to generate adjusted Wald confidence intervals is uncommon, which adds value. Users set the population parameters as well as confidence level, sample size, and number of samples which allows students to see how small changes impact the confidence intervals produced. Students can also see the numerical value of each interval and the exact percentage of intervals that contain the mean or proportion, while the sort feature helps visualize how many intervals do not contain the parameter of interest. Some excellent investigative, problem-solving questions matching this applet are in the associated books (see Overview).
Ease of Use Concerns:
There are no instructions or supporting documents on the site, so that students who are able to run the applet may not know what to look for in terms of understanding.
Ease of Use Strengths:
The boxes and buttons are well-labeled making the applet fairly intuitive. Because this applet is focused only on confidence intervals, students should be able to manipulate the parameters and run the applet. In addition, students can experiment to discover the concepts involved.
Potential Effectiveness Concerns:
Unless teachers have the textbooks, they will have to create lessons or activities to accompany the applet for students to receive the most benefit. Without it, students would need explicit instructions to use the applet independently, as none are provided on the web page itself.
Potential Effectiveness Strengths:
The ability to manipulate population parameters, sample size, and confidence level and to see immediate changes will help students deepen their understanding of confidence and confidence intervals. Users can easily see how confidence intervals behave in the long run as well as what impact parameters have on them.
Content Quality Rating:
4
Ease of Use Rating:
4
Potential Effectiveness Rating:
4
Source Code Available:
Source Code Available
Intended User Role:
Learner, Teacher
Material Type:
Resource Type:
Statistical Topic: