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# Peer Review

## Simulating Confidence Intervals

by Beth Chance , Allan Rossman

## Ratings

### Overall Rating:

Content Quality:
Effectiveness:
Ease of Use:
 Reviewed: Feb 22, 2007 by Statistics Editorial Board Overview: 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. Learning Goals: This applet can help students develop an understanding of confidence intervals by exploring the impact of sample size, confidence level, etc., on the width of confidence intervals for means and proportions and may be useful for understanding the need for the t-distribution and the adjusted Wald confidence interval. Target Student Population: This applet is appropriate for introductory statistics students or any statistics class that is going to discuss confidence intervals. Prerequisite Knowledge or Skills: Students need familiarity with means and proportions, an introduction to confidence intervals, and understanding of the Normal distribution, sampling distributions, and the Central Limit Theorem to make the best use of this applet. Type of Material: Java Applet Recommended Uses: This applet could be used as part of a class demonstration or lecture. Instructors who have the associated ISCAM or Workshop Statistics textbooks could assign the module as homework; otherwise, teachers will need to give their own instructions for assigned activities. Technical Requirements: Java enabled web browser

### Content Quality

Rating:
 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). 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.

### Potential Effectiveness as a Teaching Tool

Rating:
 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. 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.

### Ease of Use for Both Students and Faculty

Rating:
 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. 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.

Other Issues and Comments: This applet provides a useful visual representation of calculating confidence intervals for means and proportions and can help enhance students understanding of confidence and confidence intervals. Teachers without the associated textbooks will have to spend some time preparing materials and activities to accompany the applet so that students get the most benefit.
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