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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> <meta name="author" content="Douglas Chinn" /> </head> <body> <div> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-weight:bold;font-size:11pt;font-family:'Calibri'">Online Participation Topic: Week 5</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'"> For week 5, the online participation topic is on confidence intervals. We basically want to find the mean of a population (µ) by taking a sample and inferring a range of µ from the sample’s properties. Let</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">N = the population size</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">n = the sample size</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">µ = the population mean</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'"> = the sample mean</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">σ = the population standard deviation</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">s = the sample standard deviation</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">The sample’s properties (n, , s) are known or can be computed. The population’s properties (N, µ, σ) are the unknowns. However, n << N (usually).</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'"> Sometimes σ is known. If this is the case, we can compute a z-score:</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">z = =</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">If σ is unknown, we then compute a t-score</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">t = =</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">k is a measure of the number of standard deviations from the mean. By choosing an appropriate value of z or t, we can construct a “confidence interval” about the mean</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">( – k) < µ < ( + k)</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">If we let z = 1.645 so that 90% of a normal distribution would fall between +/-1.645σ of the mean, then the above inequality would be a 90% confidence interval. This means that 90% of the time, the population µ will be inside the confidence interval constructed using the sample data.</span> </p> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> <span style="font-size:11pt;font-family:'Calibri'">For week 5:</span> </p> <ol awml:style="List Paragraph"> <li> <span></span><span style="font-size:11pt;font-family:'Calibri'">Download the Excel spreadsheet OnlineWeek2.xlsx, or OnlineWeek2Data again from Week 2.</span> </li> <li> <span></span><span style="font-size:11pt;font-family:'Calibri'">Reserve one the of the data set columns (A-V) different from the one you did for Week 2.</span> </li> <li> <span></span><span style="font-size:11pt;font-family:'Calibri'">Compute , s using Excel, and df (degrees of freedom).</span> </li> <li> <span></span><span style="font-size:11pt;font-family:'Calibri'">Find the 90% t-score using the t-distribution applet. We are not using the z-distribution because we do not know σ, the standard deviation of the population (stdev.p). Thus, we are using the t-distribution because we know only the standard deviation of the sample (stdev.s).</span> </li> <li> <span></span><span style="font-size:11pt;font-family:'Calibri'">Compute the 90% “confidence interval”.</span> </li> <li> <span></span><span style="font-size:11pt;font-family:'Calibri'">Write in words the meaning of your confidence interval.</span> <a name="_GoBack"> </a> </li> <li> <span></span><span style="font-size:11pt;font-family:'Calibri'">Post your answer to “Week 5 Discussion Group Inputs”.</span> </li> </ol> <p class="" style="text-align:left;margin-bottom:8pt" awml:style="Normal"> </p> <p> </p> </div> </body></html> ">
