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Peer Review

Confidence Interval for a Proportion

by Larry Green


Overall Numeric Rating:

1.75 stars
Content Quality: 2 stars
Effectiveness: 1.25 stars
Ease of Use: 2.75 stars
Reviewed: Feb 23, 2010 by Statistics Editorial Board
Overview: This Java applet tutorial provides a series of word problems on determining confidence intervals. Each problem prompts the user to input the steps for determining a confidence interval for a proportion. Hints are provided whenever the user enters an incorrect value. Once the steps are completed, a statement summarizing the interval obtained is displayed. The applet is supported by an explanation of the steps in creating confidence intervals
Type of Material: Java applet
Recommended Uses: Give students practice at reading a "real-world" example and pulling out the relevant information for a CI for a proportion.
Technical Requirements: Java and a calculator
Identify Major Learning Goals: To learn to create confidence intervals for a single proportion in the context of a story.
Target Student Population: Introductory statistics (high school or college)
Prerequisite Knowledge or Skills: Familiarity with the CI formula for a single population proportion; a hand calculator is also required.

Evaluation and Observation

Content Quality

Rating: 2 stars
Strengths: The applet generates several real-world examples, giving students practice at statistics in context. It appears that 8-10 different real-world scenarios are available in the random rotation. The applet allows for almost any number of decimal places the user wishes to input.
Concerns: The applet doesn't "do" anything else. Students must type in n and x, then compute p-hat by hand and type that in, then read the confidence coefficient off of a chart, then manually compute the ME, and then manually compute the endpoints of the CI. A pop-up window appears at the end of the sequence reading, "A 90% confidence interval for the mean [sic] is between .xx and .xx" (whatever the correct endpoints are). The applet identifies the number of successes in the sample as r, which is peculiar. Also, the applet identifies the sample proportion as p rather than p-hat, which will confuse students whose textbooks use p to denote a population proportion. It is not clear that the user should press the “ENTER” key after typing the first answer. The confidence interval formula is not given until the student makes a mistake. The student is not asked to find Z-sub c values – and the meaning of these values is not explained. Nor does the table allow for confidence levels other than 80%, 90%, 95% and 99%. Students are not asked to interpret the confidence intervals after they find them. Basically all the applet does is check a student’s ability to use a calculator correctly.

Potential Effectiveness as a Teaching Tool

Rating: 1.25 stars
Strengths: This module checks whether students understand how to use the calculator correctly to calculate a confidence interval for a proportion.
Concerns: The applet does nothing to enhance understanding of the confidence interval concept, nor does give the opportunity to interpret an interval in context. The applet emphasizes rote computation over understanding. A student comes away feeling they "know confidence intervals" because s/he was able to correctly plug into a CI formula.

Ease of Use for Both Students and Faculty

Rating: 2.75 stars
Strengths: The instructions at the top of the web page are clear, even alerting the user to slightly nonstandard notation. The applet is simple and easy to use. If a student makes an error, a pop-up window alerts the student and suggests a remedy. (E.g. if a student gives 90 for the confidence coefficient rather than .90, a prompt reads "Don't forget that c is a proportion, so divide by 100.")
Concerns: The overall style of the page is sloppy -- three different fonts, a clumsy look reminiscent of websites 10 years ago. The applet has little or no graphics, and so it not visually appealing and does not have clear instructions. The lack of graphics may be a good thing because that may avoid distractions for the students. The applet gets repetitive quickly, in that students are just computing CIs over and over again.

Other Issues and Comments: Overall, this is a "worst practices" applet, teaching students that statistics is all about rote computation and that understanding of the confidence concept or proper interpretation of a CI in context aren't as important as step-by-step calculation. I would *never* use this applet, and I'd strongly recommend against anyone else using it. There is a link at the bottom of the tutorial to a page “Information on finding the confidence interval for a proportion.” This page begins with an error in that it state the formula for a Confidence Interval for a population mean is X-bar plus/minus Zc *s / square root of n. But it should be tc, since when we use s instead of sigma, the sampling distribution is NOT normal, but instead t. The use of the words “large sample size” does not take care of this. I am extremely uncomfortable with all the links to this author’s discussions of ‘point estimation’ and other confidence intervals, etc. He is sloppy with his use of terms and notation and his definitions. I would prefer such links be removed if this tutorial is going to remain in the Merlot archives.