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827SamplingReesesPieces.docx
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Sampling & normal distribution
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<!DOCTYPE html PUBLIC "-//ABISOURCE//DTD XHTML plus AWML 2.2//EN" "http://www.abisource.com/2004/xhtml-awml/xhtml-awml.mod"><html xmlns="http://www.w3.org/1999/xhtml" xmlns:awml="http://www.abisource.com/2004/xhtml-awml/"> <head> <meta http-equiv="Content-Type" content="application/xhtml+xml; charset=UTF-8" /> <title> Abiword HTML Document </title> </head> <body> <div> <p> <a name="_Hlk483215276"> <span style="font-size:14pt;font-family:'Impact'">Sampling Distributions</span> </a> </p> <p> </p> <div style="background-color: #ffffff; border: solid; clear: none;"> <span></span><span style="font-size:11pt;font-family:'Cambria'">Reese’s Pieces candies come in three colors: orange, brown, and yellow. Which color do you think has more candies in a package: orange, brown or yellow? I am asking you to</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">guess,</span><span style="font-size:11pt;font-family:'Cambria'">based on this picture, or on your own experience.</span> <ul> <li> <span></span><span style="font-size:11pt;font-family:'Cambria'">From my own experience I think that I pull out a lot of brown M&M’s. If I had to guess based off this picture I would choose orange because it seems like it makes up about 50% percent of M&M’s shown.</span> </li> </ul> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p> </p> </div> <p> <span style="font-size:11pt;font-family:'Cambria'">Math 243</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <img style="width:184.1mm" src="827SamplingReesesPieces.docx.txt_files/rId7.png" title="" alt="" align="left" /><span></span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">Guess</span><span style="font-size:11pt;font-family:'Cambria'"> the proportion of each color in a bag. Give your answers as percentages:</span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="text-indent:18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'">Orange______48%______ Brown______30%______ Yellow_____22%________</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Let’s think about the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">orange</span><span style="font-size:11pt;font-family:'Cambria'"> candies. Suppose we had an unimaginably large bag of Reese’s Pieces. If each student in our class took a sample of 25 Reese’s Pieces, would you expect every student to have the same number of</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">orange</span><span style="font-size:11pt;font-family:'Cambria'"> candies in their sample? Explain.</span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> <a name="_GoBack"> </a> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Let’s say that 10 students each took a sample of 25 Reese’s Pieces. Write down the number of orange candies you might expect in each of these 10 samples, based on your answer to question 2:</span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt"> <a name="_Hlk483215834"> <span style="font-size:11pt;font-family:'Cambria'">________ ________ ________ ________ ________ ________ ________ ________ ________ ________</span> </a> </p> <p style="margin-left:18.000000pt"> </p> <div style="background-color: #ffffff; border: solid; clear: none;"> <p style="margin-left:18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'">Of course, the number of orange candies in each sample shouldn’t be the same. These numbers represent the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">expected</span><span style="font-size:11pt;font-family:'Cambria'"></span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">variability</span><span style="font-size:11pt;font-family:'Cambria'"> you would expect to see in the number of orange candies in 10 samples of 25 pieces each.</span> </p> </div> <p style="margin-left:18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Write your answers to the previous problem as</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">proportions</span><span style="font-size:11pt;font-family:'Cambria'">—either as decimals or percentages:</span> <p> </p> <p> </p> <p style="margin-left:18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'">________ ________ ________ ________ ________ ________ ________ ________ ________ ________</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">The proportions in question 5 are called</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">sample statistics.</span><span style="font-size:11pt;font-family:'Cambria'">This is a generic term – a</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">sample statistic</span><span style="font-size:11pt;font-family:'Cambria'"> is anything we use to summarize a sample. In this case, we could also call these</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">sample proportions</span><span style="font-size:11pt;font-family:'Cambria'">, because we computed a</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">proportion</span><span style="font-size:11pt;font-family:'Cambria'"> to summarize each sample.</span> </p> <p> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">We use the term</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">population parameter</span><span style="font-size:11pt;font-family:'Cambria'"> to refer to the value that summarizes the whole population. In this case, we are exploring the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">population proportion</span><span style="font-size:11pt;font-family:'Cambria'">of orange Reese’s Pieces.</span> </p> <p> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">For the purposes of the next five questions, proceed as though you and all the other students in the class</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">actually</span><span style="font-size:11pt;font-family:'Cambria'"> drew a sample of 25 candies each.</span> </p> <p> </p> <p> <span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">Notation:</span> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">The</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">population proportion</span><span style="font-size:11pt;font-family:'Cambria'"> is usually denoted by a lower-case</span><span style="font-weight:bold;font-size:11pt;font-family:'Arial'">p</span><span style="font-size:11pt;font-family:'Cambria'">.</span> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">The</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">sample proportion</span><span style="font-size:11pt;font-family:'Cambria'"> is usually denoted by a lower-case p with a “hat” on it</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">:</span><span style="font-weight:bold;font-size:11pt;font-family:'Arial'">p̂.</span><span style="font-size:11pt;font-family:'Arial'"></span><span style="font-size:11pt;font-family:'Cambria'">We say “p-hat”.</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Do we know the value of the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">population parameter</span><span style="font-size:11pt;font-family:'Cambria'"></span><span style="font-weight:bold;font-size:11pt;font-family:'Arial'">p</span><span style="font-size:11pt;font-family:'Cambria'"> (the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">population proportion</span><span style="font-size:11pt;font-family:'Cambria'"></span> <p> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Do we know the values of the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">sample statistics</span><span style="font-weight:bold;font-size:11pt;font-family:'Arial'">p̂</span><span style="font-size:11pt;font-family:'Cambria'">’s (the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">sample proportions</span><span style="font-size:11pt;font-family:'Cambria'"> of orange candies in each student’s sample of n = 25 candies)?</span> <p awml:style="List Paragraph"> </p> <p> </p> <p awml:style="List Paragraph"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'"></span> <p style="margin-left:18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'"></span></p> <p> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Does the value of the population parameter</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">change</span><span style="font-size:11pt;font-family:'Cambria'"></span> <p> <span style="font-size:11pt;font-family:'Cambria'"></span></p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Does the value of the sample statistic</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">change</span><span style="font-size:11pt;font-family:'Cambria'"></span> <p> <span style="font-size:11pt;font-family:'Cambria'"></span></p> <p> <span style="font-size:11pt;font-family:'Cambria'">Instead, we will simulate the activity using a web applet. Go to</span> </p> <p> </p> <p> <a href="http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=1"><span style="font-size:11pt;font-family:'Cambria'">http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=1</span></a><span style="font-size:11pt;font-family:'Cambria';color:#0070c0"></span></p> <p> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">You will see a cartoon container of colored candies: this represents the POPULATION.</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'"></span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">You will see that the probability of orange is set at 0.5, so this is the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">population parameter,</span><span style="font-size:11pt;font-family:'Cambria'">which in this case is the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">population proportion</span><span style="font-weight:bold;font-size:11pt;font-family:'Arial'">p</span><span style="font-size:11pt;font-family:'Cambria'">. (People who have counted lots of Reese’s Pieces came up with this number, for example,</span><a href="http://theskepticalstatistician.blogspot.com/2012/09/the-reeses-rainbow-validating-childs.html"><span style="font-size:11pt;font-family:'Cambria'">this guy</span></a><span style="font-size:11pt;font-family:'Cambria'">).</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">How does 0.5 compare to the proportion of orange candies in your guess in question 2? Were you close?</span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p> <span style="font-size:11pt;font-family:'Cambria'"></span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'">On the left side of the Reese’s Pieces web page, change “Number of orange” to “Proportion of orange”:</span><span></span></p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <img style="width:110.6mm" src="827SamplingReesesPieces.docx.txt_files/rId10.png" title="" alt="" align="right" /> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">Click on the “</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">Draw Samples</span><span style="font-size:11pt;font-family:'Cambria'">” button. One sample of 25 candies will be taken and the proportion of orange candies in this sample is displayed in blue (under the candy machine, it will say something like, for example,</span><span style="font-weight:bold;font-size:14pt;font-family:'Arial';color:#0000ff">p̂</span><span style="font-size:13.5pt;font-family:'Helvetica';color:#0000ff"> = 0.640,</span><span style="font-size:11pt;font-family:'Cambria'">depending on your sample and sample proportion), and also plotted on the graph.</span> </p> <p> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">Repeat this two or three more times.</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Do you get the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">same</span><span style="font-size:11pt;font-family:'Cambria'"> or</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">different</span><span style="font-size:11pt;font-family:'Cambria'"></span> <p> </p> <p> </p> <p> <span style="font-size:11pt;font-family:'Cambria'"></span></p> <span></span><span style="font-size:11pt;font-family:'Cambria'">In general, about how close is each</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">sample statistic</span><span style="font-size:11pt;font-family:'Cambria'"> (sample proportion,</span><span style="font-weight:bold;font-size:11pt;font-family:'Arial'">p̂</span><span style="font-size:11pt;font-family:'Cambria'">) to the</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">population parameter</span><span style="font-size:11pt;font-family:'Cambria'">(population proportion,</span><span style="font-weight:bold;font-size:11pt;font-family:'Arial'">p</span><span style="font-size:11pt;font-family:'Cambria'"></span> <p> </p> <p> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Why aren’t the values of the sample proportions the</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">SAME</span><span style="font-size:11pt;font-family:'Cambria'"> as the population proportion (0.5)?</span> <p> </p> <p> <span style="font-size:11pt;font-family:'Cambria'"></span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'">Unclick the</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'"> “Animate”</span><span style="font-size:11pt;font-family:'Cambria'">box and change “</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">Number of samples</span><span style="font-size:11pt;font-family:'Cambria'">” to 100.</span> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">Click the “</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">Draw Samples”</span><span style="font-size:11pt;font-family:'Cambria'"> button, and turn your attention to the resulting distribution of sample proportions. (This is the graph with the dots below the candy machine.)</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <div style="background-color: #ffffff; border: solid; clear: none;"> <p style="text-align:center"> <span style="font-size:11pt;font-family:'Cambria'">This distribution is called</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">The Sampling Distribution of</span><span style="font-style:italic;font-size:11pt;font-family:'Arial'">p̂</span><span style="font-weight:bold;font-size:11pt;font-family:'Arial'">.</span> </p> </div> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt"> </p> <p style="margin-left:18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'"></span><span></span><span style="font-size:11pt;font-family:'Cambria'">How is this distribution</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">different</span><span style="font-size:11pt;font-family:'Cambria'"> from the distributions we have worked with so far?</span> <p> </p> <p> </p> <p> </p> <p> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Repeat the “Draw Samples” exercise a couple times, until you start to see the general characteristics of the distribution. Describe the</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">shape, center, and spread</span><span style="font-size:11pt;font-family:'Cambria'"> of this distribution.</span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">Now we want to know: what happens to this distribution of sample statistics as we change the number of candies in each sample (sample size)?</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'">First, change the sample size (“Number of candies”) to 10 and draw 100 samples.</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">How close is each</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">sample statistic</span><span style="font-size:11pt;font-family:'Cambria'"> to the</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">population parameter</span><span style="font-size:11pt;font-family:'Cambria'"></span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">Describe the</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">shape, center, and spread</span><span style="font-size:11pt;font-family:'Cambria'">of this distribution of sample proportions with n = 10, particularly the similarities and differences with the sampling distribution we got when n = 25.</span> <p> </p> <p> </p> <p> </p> <p> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'">Next, change the sample size to 100 and draw 100 samples.</span> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">How close is each</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">sample statistic</span><span style="font-size:11pt;font-family:'Cambria'"> to the</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">population parameter</span><span style="font-size:11pt;font-family:'Cambria'"></span><span></span><span style="font-size:11pt;font-family:'Cambria'">Describe the</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">shape, center, and spread</span><span style="font-size:11pt;font-family:'Cambria'">of the distribution of sample proportions with n = 100, particularly the similarities and differences with the sampling distributions we got when n = 10 and n = 25.</span> <p style="margin-left:18.000000pt"> </p> <p style="margin-left:18.000000pt"> </p> <p style="margin-left:18.000000pt"> </p> <p style="margin-left:18.000000pt"> </p> <p style="margin-left:18.000000pt"> </p> <p> <span style="font-size:11pt;font-family:'Cambria'">Use the table to organize and summarize your results:</span> </p> <p style="margin-left:18.000000pt"> </p> <table border="0" cellpadding="0" style="width:100%;border:0.50pt solid;border-collapse:collapse;empty-cells:show;table-layout:fixed"> <tr> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> <span style="font-weight:bold;font-size:11pt;font-family:'Cambria'">Sample Size</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> <span style="font-weight:bold;font-style:italic;font-size:11pt;font-family:'Cambria'">Shape</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'"> of Sampling Distribution</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> <span style="font-weight:bold;font-style:italic;font-size:11pt;font-family:'Cambria'">Center</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'"> of Sampling Distribution</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> <span style="font-weight:bold;font-style:italic;font-size:11pt;font-family:'Cambria'">Spread</span><span style="font-weight:bold;font-size:11pt;font-family:'Cambria'"> of Sampling Distribution</span><span style="font-size:11pt;font-family:'Cambria'">(you can give the range here, as in “from about 0.24 to about 0.76”)</span> </p> </td> </tr> <tr> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> <span style="font-size:11pt;font-family:'Cambria'">n = 10</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> </tr> <tr> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> <span style="font-size:11pt;font-family:'Cambria'">n = 25</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> </tr> <tr> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> <span style="font-size:11pt;font-family:'Cambria'">n = 100</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;border:0.50pt solid inherit"> <p style="text-align:center"> </p> </td> </tr> </table> <p> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">How well do the sample statistics resemble the population parameter? Does it depend on the sample size?</span> <p style="margin-top:6.000000pt"> </p> <p style="margin-top:6.000000pt"> </p> <p style="margin-top:6.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">What is the effect of sample size on the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">shape</span><span style="font-size:11pt;font-family:'Cambria'"></span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">What is the effect of sample size on the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">center</span><span style="font-size:11pt;font-family:'Cambria'"></span> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <span></span><span style="font-size:11pt;font-family:'Cambria'">What is the effect of sample size on the</span><span style="font-style:italic;font-size:11pt;font-family:'Cambria'">spread</span><span style="font-size:11pt;font-family:'Cambria'"></span><span></span><span style="font-size:11pt;font-family:'Cambria'">Let’s think about opinion polling. If we want to know: how a group of voters might vote, how a group of consumers feels about a product or service, how a group of students feels about a class, we might devise a question, select a sample, conduct a survey, and compute a sample proportion</span><span style="font-weight:bold;font-style:italic;font-size:11pt;font-family:'Arial'">p̂</span><span style="font-size:11pt;font-family:'Cambria'">.</span> <p class="list_paragraph" style="margin-left:18.000000pt" awml:style="List Paragraph"> </p> <p class="list_paragraph" style="margin-left:18.000000pt" awml:style="List Paragraph"> <span style="font-size:11pt;font-family:'Cambria'">How does the sampling distribution of</span><span style="font-weight:bold;font-style:italic;font-size:11pt;font-family:'Arial'">p̂</span><span style="font-style:italic;font-size:11pt;font-family:'Arial'"></span><span style="font-size:11pt;font-family:'Cambria'">help us to understand the relationship between our sample and the population? Put another way, how does the sampling distribution help us to determine how well our single sample statistic</span><span style="font-weight:bold;font-style:italic;font-size:11pt;font-family:'Arial'">p̂</span><span style="font-size:11pt;font-family:'Cambria'"> reflects the true population parameter</span><span style="font-weight:bold;font-style:italic;font-size:11pt;font-family:'Arial'">p</span><span style="font-size:11pt;font-family:'Cambria'"></span></p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> <span style="font-size:11pt;font-family:'Cambria'"></span></p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p style="margin-left:18.000000pt;text-indent:-18.000000pt"> </p> <p awml:style="footer"> </p> <p awml:style="footer"> <div> </div> <p awml:style="footer"> </p> <p awml:style="footer"> </p> </p> </div> </body></html> ">
