Last modified: 05/01/2010
Sampling Distribution of Sample Means
Downloads for this lesson plan
Introduction
Students will create sampling distributions of sample means from various distributions. They will compare and contrast their results and discuss why randomness is an important consideration in the process. They should also gain an understanding on the impact of sample size on the result.Prerequisite Experience
The Students will have demonstrated competence with navigating the Internet and keyboarding skills. They have used Tables of Random Digits and Minitab software and are familiar with their use. They will possess some basic knowledge of the use of presentation software.Teacher Prep Time
1 – 2 hours. Teachers will want to become familiar with some of the sites dealing with the topic area. It will be useful to look at the PowerPoint training videos found at Nortel LearniT (www.NortelLearniT.org). Students may be directed to these videos prior to starting their assignment if they need assistance.Project
Students will create a multimedia presentation that demonstrates their understanding of the creation and interpretation of a sampling distribution. The goal of the PowerPoint presentation is to report on their findings and describe their Extend activity.Assessment/Grading
An evaluation rubric has been provided to use in assessing the presentations.Time Management Tips
Students should be divided into groups. Rather than have each group present their entire report, choose one or two areas for them to present to the class.Lesson Plan Details
Engage
We have discussed randomness and its role in sampling and experimental design. Today we are going to rely on randomness to help us develop an understanding of the sampling distribution concept. View short video clip on randomness from Numb3rs. Recall that a sampling distribution is the distribution created from the sample statistics from many samples of the same size from the same population. We are going to explore populations that we believe may have an approximately normal shape as well as populations that we know are not normal. The question is, “What do the sampling distributions look like for each of these cases?” You will be working in groups of four for this assignment. You will be collecting data, analyzing the data using Minitab and reporting your results with a PowerPoint presentation.Explore
In this section you will be exploring properties of randomness and distributions as well as learning something about our telephone system. You will need access to the internet and Microsoft Word to record your findings. The following lists of sites are examples of the information you should be finding. You do not need to read each site in detail, but rather scan the site for interesting information. Several of the sites employ java applets to help you understand the material better. Go to LiveBinders and open your Sampling Distribution Binder. Add the following sites to your LiveBinder: These sited discuss randomness: http://www.random.org/http://en.wikipedia.org/wiki/Random_numberhttp://mathworld.wolfram.com/RandomNumber.html The Wikipedia site contains several interesting links. Check out one or two of them and add any interesting ones to your LiveBinder. The following sites discuss Sampling Distributions: http://onlinestatbook.com/stat_sim/sampling_dist/index.htmlhttp://en.wikipedia.org/wiki/Sampling_distributionhttp://www.stat.tamu.edu/~west/ph/sampledist.html This site describes a phone number: http://en.wikipedia.org/wiki/Telephone_number Summarize your findings in your word document for later use in your presentation. Also note any additional sites you may have discovered during your exploration. Then add your word document to your LiveBinder.Explain
Prior to proceeding to the data collection and analysis activity, it is probably a good idea to make sure you understand the major concepts you have encountered thus far. In your own words, describe or explain:1. Randomness and Random Numbers
2. Data Distribution
3. Random Sample
4. Sample Statistic
5. Normal Distribution
6. Sampling Distribution
Discuss your answers with the other members of your group. Prepare a smooth document that addresses all six topics and then copy and paste your comments into the Sampling Distribution Wiki on the class SharePoint site. Be sure to identify all members of your group in your post. Look at any other posts that may be in the wiki and comment on them. If you are the first, be sure to check back often so that every group gets to comment on other posts.Elaborate
By now you should have a pretty good idea what we mean by randomness and sampling distribution. Work with your group to complete Activity 7.2a, Phone Numbers and Center. You will need your cell phone, a computer with Minitab and Microsoft word, and a table of random digits to complete this activity. I will send you an electronic copy of this activity via SynchronEyes so you can work directly on it.
After you have completed this activity, insert your completed worksheet in your LiveBinder.
The final step of this activity is to create a PowerPoint presentation that summarizes your findings. Include a discussion of randomness, sampling distributions, and phone numbers as an introduction to your presentation.
Phone Numbers and CenterActivity 7.2a Name: ___________________________________ Block: _____ Date: __________________ What you’ll need: Table of random digits, calculator, cell phone, computer Directions: Complete the activity as described below. Answer the questions in your Word document and then use the findings from your activity to prepare a PowerPoint presentation. Each member of the group should complete steps 1 through 9, and the group should prepare the PowerPoint. 1. Based on your internet research, what do the different parts of a phone number represent? How are these numbers assigned, and what, if any, historical significance is associate with each part? Based on your research, which part of the phone number could be assumed to be randomly generated? 2. What would a distribution of the digits used for the random part of the phone number look like? What is the mean and standard deviation of this distribution? 3. Using your table of random digits, select 10 phone numbers from your cell phone phonebook and write down the last four digits of each in the table on the next page of this activity. 4. Find the mean of each phone number. You should have 10 means. Record them in the table. 5. Group your phone numbers by pairs (first and second, third and fourth, etc) making 8 digits. Find the mean of each pair. You should have 5 means. Record them in the table. 6. Group your phone numbers into two groups, first through fifth and sixth through tenth. Find the mean of each group. You should have 2 means. Record them in the table. 7. Send me your completed tables on SynchronEyes. I will consolidate the data and send it back to you so you can create the class dot plots with Minitab. 8. Using Minitab, create class dot plots for the individual means, the means of each pairs, and the means of each half. You should create three dot plots. Paste your dot plots into your Word document. 9. Compare and contrast the three dot plots. 10. Based on our knowledge of sampling distributions, you should be able to predict the mean and standard deviation of each plot. Calculate the predicted values and compare them to the actual values calculated by Minitab for our data. How do the two sets of values compare? How can you explain any differences? 11. Create a PowerPoint presentation that summarizes your research and your findings from this activity.
Data Table
Phone Number | Mean of each | Mean of each pair | Mean of each half |
Evaluate
Evaluation Rubric| Criteria | Unsatisfactory | Needs Improvement | Satisfactory | Exemplary |
| Research | Limited research, from limited sources | Somewhat well researched from somewhat varied sources. | Well researched, from various sources | Thorough research from varied sources presenting different points of view |
| Planning | Limited planning evident | Some planning evident | Planning evident | Thorough planning evident |
| Content | Lacks detail | Some detail | Good detail | Excellent detail |
| Technology Use to Demonstrate Understanding | Technology use with little purpose | Technology use with some purpose | Technology use with purpose | Intuitive technology use with specific purpose |
| Overall Final Project | Inconsistent and inappropriate aesthetics and technical functionality | Somewhat consistent and appropriate aesthetics and technical functionality | Consistent and appropriate aesthetics and technical functionality | Consistent, creative and appropriate aesthetics and technical functionality |
Extend
Chose one of the following:
1. Minitab worksheet “What is a Sampling Distribution?” explores creating and analyzing sampling distributions created from a true uniform distribution. Complete this worksheet and compare those results to your results from the phone number distribution.
2. Several of the web sites you visited contained applets that generated sampling distributions from different populations. Use one of these applets to generate sampling distributions of different sizes from the uniform distribution and compare your results to your results from the phone number distribution.
3. Use one of the web sites to create sampling distributions from highly skewed populations. Predict the results and analyze how closely your predictions come to the applet results.
4. Assuming that the table of random digits is truly random, the digits should represent a uniform distribution. Take 100 samples of size 30 and compare the sampling distribution to the theoretical.