{"id":5196,"date":"2022-08-18T21:12:30","date_gmt":"2022-08-18T21:12:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=5196"},"modified":"2022-08-18T21:13:29","modified_gmt":"2022-08-18T21:13:29","slug":"9b-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/9b-preview\/","title":{"raw":"9B Preview","rendered":"9B Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to be able to identify whether a summary measure is a parameter or a statistic, determine the appropriate type of plot for a given dataset, simulate sample proportions of random samples of a given size from a population with known p, describe and interpret features of a sampling distribution of sample proportions, and calculate the standard deviation of a sample proportion.\r\n\r\nThe 2020 November presidential election in the United States had one of the highest voter turnout rates in recent history: 66.7% of the voting-eligible population voted for a candidate for president.[footnote] United States Elections Project. (2020, December 7). <em>2020 November general election turnout rates.<\/em> http:\/\/www.electproject.org\/2020g[\/footnote]\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 1<\/h3>\r\nIs the value 66.7% a parameter or a statistic?\r\n<ol>\r\n \t<li>Parameter, since it summarizes an entire population<\/li>\r\n \t<li>Parameter, since it summarizes a sample from the population<\/li>\r\n \t<li>Statistic, since it summarizes an entire population<\/li>\r\n \t<li>Statistic, since it summarizes a sample from the population<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 2<\/h3>\r\nTrue or false: If you take a simple random sample of 1,000 individuals from the U.S. voting-eligible population and ask each individual whether they voted in the 2020 November presidential election, 667 of them will answer yes.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 3<\/h3>\r\nSuppose you plan to take a simple random sample of 10 individuals from the U.S. voting-eligible population and ask each individual whether they voted in the 2020 November presidential election.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>What would be the appropriate plot to display these data?\r\n<ol>\r\n \t<li>Scatterplot<\/li>\r\n \t<li>Boxplot<\/li>\r\n \t<li>Bar graph<\/li>\r\n \t<li>Normal curve<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Do you think it is very likely for your sample proportion to be 0.6? Explain.<\/li>\r\n \t<li>Do you think it is very likely for your sample to have [latex] \\hat{p} = 0.3 [\/latex]? Explain.<\/li>\r\n<\/ol>\r\n<\/div>\r\nGo to the DCMP Sampling Distribution of the Sample Proportion tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/SampDist_Prop\/\">https:\/\/dcmathpathways.shinyapps.io\/SampDist_Prop\/<\/a>. You will use this tool to simulate taking random samples of 10 individuals from the U.S. voting-eligible population:\r\n<ul>\r\n \t<li aria-level=\"1\">Set the Population Proportion to [latex]p= 0.67[\/latex].<\/li>\r\n \t<li aria-level=\"1\">Set the Sample Size to [latex]n = 10[\/latex].<\/li>\r\n \t<li aria-level=\"1\">Simulate taking 1,000 random samples of size 10 by selecting \u201c1,000\u201d and clicking \u201cDraw Sample(s).\u201d<\/li>\r\n<\/ul>\r\nThe \u201cSampling Distribution of Sample Proportion\u201d graph at the bottom of the tool displays the distribution of the 1,000 sample proportions from your random samples.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 4<\/h3>\r\nUse the \u201cSampling Distribution of Sample Proportion\u201d graph to approximate the proportion of the simulated samples with [latex]\\hat{p}= 0.6[\/latex].\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 5<\/h3>\r\nUse the bar above [latex]\\hat{p}= 0.5[\/latex] on the \u201cSampling Distribution of Sample Proportion\u201d graph to complete the following sentence:\r\n\r\nFor a sample of 10 individuals from the U.S. voting-eligible population, the approximate probability that exactly ______ individuals in the sample voted in the 2020 November presidential election is ______ .\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 6<\/h3>\r\nThe standard deviation of simulated sample proportions should be close to 0.15. Which of the following is a correct interpretation of this value?\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>We would expect a typical sample proportion of individuals who voted in the 2020 November presidential election to be around 0.15.<\/li>\r\n \t<li>We would expect a typical sample proportion of individuals who voted in the 2020 November presidential election in a random sample of size 10 to be about 0.15 away from 0.67.<\/li>\r\n \t<li>All sample proportions of individuals who voted in the 2020 November presidential election in random samples of size 10 will be 0.15 away from 0.67.<\/li>\r\n \t<li>About 50% of sample proportions of individuals who voted in the 2020 November presidential election in random samples of size 10 will be between 0.52 and 0.82.<\/li>\r\n<\/ol>\r\n<\/div>\r\nRather than using simulation, we can use mathematical theory to derive expressions for the mean and standard deviation of the sampling distribution of the sample proportion.\r\n\r\nKeep these properties in mind as you answer the remaining questions in this preview assignment.\r\n<div class=\"textbox\">\r\n\r\nSampling Distribution of the Sample Proportion\r\n\r\nWhen taking many random samples of size n from a population distribution with population proportion p:\r\n<ul>\r\n \t<li aria-level=\"1\">The mean of the distribution of sample proportions is [latex]p[\/latex].<\/li>\r\n \t<li>The standard deviation of the distribution of sample proportions is [latex]\\sqrt{\\frac{p(1-p)}{n}}[\/latex]. Type your textbox content here.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 7<\/h3>\r\nUse a formula to calculate the standard deviation of sample proportions when taking random samples of size 10 from a population where [latex]p= 0.67[\/latex].\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<p>Preparing for the next class<\/p>\n<p>In the next in-class activity, you will need to be able to identify whether a summary measure is a parameter or a statistic, determine the appropriate type of plot for a given dataset, simulate sample proportions of random samples of a given size from a population with known p, describe and interpret features of a sampling distribution of sample proportions, and calculate the standard deviation of a sample proportion.<\/p>\n<p>The 2020 November presidential election in the United States had one of the highest voter turnout rates in recent history: 66.7% of the voting-eligible population voted for a candidate for president.<a class=\"footnote\" title=\"United States Elections Project. (2020, December 7). 2020 November general election turnout rates. http:\/\/www.electproject.org\/2020g\" id=\"return-footnote-5196-1\" href=\"#footnote-5196-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 1<\/h3>\n<p>Is the value 66.7% a parameter or a statistic?<\/p>\n<ol>\n<li>Parameter, since it summarizes an entire population<\/li>\n<li>Parameter, since it summarizes a sample from the population<\/li>\n<li>Statistic, since it summarizes an entire population<\/li>\n<li>Statistic, since it summarizes a sample from the population<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 2<\/h3>\n<p>True or false: If you take a simple random sample of 1,000 individuals from the U.S. voting-eligible population and ask each individual whether they voted in the 2020 November presidential election, 667 of them will answer yes.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 3<\/h3>\n<p>Suppose you plan to take a simple random sample of 10 individuals from the U.S. voting-eligible population and ask each individual whether they voted in the 2020 November presidential election.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>What would be the appropriate plot to display these data?\n<ol>\n<li>Scatterplot<\/li>\n<li>Boxplot<\/li>\n<li>Bar graph<\/li>\n<li>Normal curve<\/li>\n<\/ol>\n<\/li>\n<li>Do you think it is very likely for your sample proportion to be 0.6? Explain.<\/li>\n<li>Do you think it is very likely for your sample to have [latex]\\hat{p} = 0.3[\/latex]? Explain.<\/li>\n<\/ol>\n<\/div>\n<p>Go to the DCMP Sampling Distribution of the Sample Proportion tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/SampDist_Prop\/\">https:\/\/dcmathpathways.shinyapps.io\/SampDist_Prop\/<\/a>. You will use this tool to simulate taking random samples of 10 individuals from the U.S. voting-eligible population:<\/p>\n<ul>\n<li aria-level=\"1\">Set the Population Proportion to [latex]p= 0.67[\/latex].<\/li>\n<li aria-level=\"1\">Set the Sample Size to [latex]n = 10[\/latex].<\/li>\n<li aria-level=\"1\">Simulate taking 1,000 random samples of size 10 by selecting \u201c1,000\u201d and clicking \u201cDraw Sample(s).\u201d<\/li>\n<\/ul>\n<p>The \u201cSampling Distribution of Sample Proportion\u201d graph at the bottom of the tool displays the distribution of the 1,000 sample proportions from your random samples.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 4<\/h3>\n<p>Use the \u201cSampling Distribution of Sample Proportion\u201d graph to approximate the proportion of the simulated samples with [latex]\\hat{p}= 0.6[\/latex].<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 5<\/h3>\n<p>Use the bar above [latex]\\hat{p}= 0.5[\/latex] on the \u201cSampling Distribution of Sample Proportion\u201d graph to complete the following sentence:<\/p>\n<p>For a sample of 10 individuals from the U.S. voting-eligible population, the approximate probability that exactly ______ individuals in the sample voted in the 2020 November presidential election is ______ .<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 6<\/h3>\n<p>The standard deviation of simulated sample proportions should be close to 0.15. Which of the following is a correct interpretation of this value?<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>We would expect a typical sample proportion of individuals who voted in the 2020 November presidential election to be around 0.15.<\/li>\n<li>We would expect a typical sample proportion of individuals who voted in the 2020 November presidential election in a random sample of size 10 to be about 0.15 away from 0.67.<\/li>\n<li>All sample proportions of individuals who voted in the 2020 November presidential election in random samples of size 10 will be 0.15 away from 0.67.<\/li>\n<li>About 50% of sample proportions of individuals who voted in the 2020 November presidential election in random samples of size 10 will be between 0.52 and 0.82.<\/li>\n<\/ol>\n<\/div>\n<p>Rather than using simulation, we can use mathematical theory to derive expressions for the mean and standard deviation of the sampling distribution of the sample proportion.<\/p>\n<p>Keep these properties in mind as you answer the remaining questions in this preview assignment.<\/p>\n<div class=\"textbox\">\n<p>Sampling Distribution of the Sample Proportion<\/p>\n<p>When taking many random samples of size n from a population distribution with population proportion p:<\/p>\n<ul>\n<li aria-level=\"1\">The mean of the distribution of sample proportions is [latex]p[\/latex].<\/li>\n<li>The standard deviation of the distribution of sample proportions is [latex]\\sqrt{\\frac{p(1-p)}{n}}[\/latex]. Type your textbox content here.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 7<\/h3>\n<p>Use a formula to calculate the standard deviation of sample proportions when taking random samples of size 10 from a population where [latex]p= 0.67[\/latex].<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-5196-1\"> United States Elections Project. (2020, December 7). <em>2020 November general election turnout rates.<\/em> http:\/\/www.electproject.org\/2020g <a href=\"#return-footnote-5196-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":6,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5196","chapter","type-chapter","status-publish","hentry"],"part":5175,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5196","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/574340"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5196\/revisions"}],"predecessor-version":[{"id":5198,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5196\/revisions\/5198"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5175"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5196\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5196"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5196"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5196"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}