This applet simulates drawing samples of Reeses Pieces from a candy machine. Users set the sample size, number of samples, and theta, the population proportion of orange pieces. The applet keeps track of each sample and displays a dotplot of the sample proportion of orange pieces. Users can also count the number of samples below, above, or between two proportions and superimpose the normal distribution curve on the dotplot. The animation option can be turned off when selecting larger sample sizes. Instructions and activities for this applet can be found in the textbook Investigating Statistical Concepts, Applications, and Methods (ISCAM) in Investigations 4.3.1 on page 301 and 4.3.2 on page 309. This applet also supplements Workshop Statistics: Discovery with Data, 2nd edition, Activities 16-2 and 16-3. For more information about this book, go to http://www.rossmanchance.com/ws2/index.html. Additional materials written for this applet can be found at http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/Materials_High_School_Teachers/CI%20for%20prop%20reeses%20pieces.pdf.
Type of Material:
This applet could be used as part of a class demonstration or lecture in which teachers first run the activity using real Reeses Pieces, then use the applet to simulate a larger number of samples (e.g. 500). 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.
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Identify Major Learning Goals:
This applet can help familiarize students with the concepts of sampling variability and sampling distribution, in particular, the sampling distribution of a sample proportion. It can also demonstrate that normality for this distribution depends on sample size and population proportion as well as show students how to calculate tail probabilities.
Target Student Population:
This applet is appropriate for introductory statistics students or any statistics class that is going to discuss sampling distributions.
Prerequisite Knowledge or Skills:
Students must be familiar with random sampling, the normal distribution, and have some knowledge of sampling distributions of proportions to make best use of this applet.
The simulation is an excellent visual presentation of the sampling process. The applet allows users to adjust sample size, number of samples, and population proportion and accurately displays the dotplot of the sample proportions. The ability to find tail probabilities and probabilities between sample proportions is nice, and the option to overlay the normal curve is helpful for demonstrating whether the sample size is large enough (whether n*theta and n*(1-theta) meet conditions) for the Central Limit Theorem to hold. It is also helpful to be able turn the animation off for drawing large numbers of samples. The associated textbooks provide some excellent investigative, problem-solving questions that are designed for use with this applet (see Overview).
Theta here refers to the population proportion, however, it is a more common notation for a general population parameter; this could be confusing for students. On first use, users might not be aware that theta represents the proportion of orange Reeses Pieces.
The applet shows only one graph at a time, so students cannot compare graphs of distributions with different sample sizes and values of theta to see how well the central limit theorem would work. The applet does not store the values of the sample proportions in a data table, so users cannot copy it into another software package.
The site does not give directions or explain what is happening statistically, so instructors who do not have the accompanying textbooks need to be very clear about what the students need to do.
Potential Effectiveness as a Teaching Tool
This applet allows students to take a large number of samples quickly and see the results. Students will be able to visualize a sampling distribution and see how it approaches normality. The ability to make adjustments in the samples and visuals provided should help students deepen their understanding of sampling distributions. This could be done in class relatively quickly to show some of the more salient aspects of sampling distributions.
Seeing the p-value (tail probabilities) without talking about what it means can be helpful background to students before they get to statistical inference.
Teachers without the accompanying textbooks will have to create their own materials around this applet to use it in class. These teachers would also need to give students explicit instructions if this applet were assigned outside of the classroom.
Given that Hershey's does not tell consumers the proportion of different colored pieces, students and instructors might wonder where the default, theta = 0.45, came from.
Ease of Use for Both Students and Faculty
This applet is fairly intuitive and easy to use with well-labeled boxes and buttons. Because this applet is focused only on sampling distributions of proportions, students should be able to manipulate the parameters and run the applet. For those who have worked with similar applets, the learning curve for this applet is small.
Due to the absence of any guidance on the page, students may be able to change the parameters and run the applet, but not know what to look for in terms of understanding. Instructors need to make sure their students know what to do.
Other Issues and Comments:
This applet provides a useful way for introducing sampling distributions of proportions. The various display options help students deepen their understanding of sampling and lead to the Central Limit Theorem. The associated textbooks provide valuable activities, but teachers without the books will have to create their own materials around this applet.
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