{"id":241,"date":"2022-06-16T17:47:09","date_gmt":"2022-06-16T17:47:09","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&#038;p=241"},"modified":"2022-06-16T17:49:30","modified_gmt":"2022-06-16T17:49:30","slug":"random-sampling-background-youll-need","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/random-sampling-background-youll-need\/","title":{"raw":"Random Sampling: Background You'll Need 1","rendered":"Random Sampling: Background You&#8217;ll Need 1"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Goals<\/h3>\r\nIn this support activity you\u2019ll become familiar with the following:\r\n<ul>\r\n \t<li>Use technology to create a dotplot from a dataset.<\/li>\r\n \t<li>Answer questions about a variable using a dotplot.<\/li>\r\n \t<li>Use a random number generator to select a random sample.<\/li>\r\n \t<li>Anticipate sample-to-sample variability.<\/li>\r\n<\/ul>\r\nYou will also have an opportunity to refresh the following skills:\r\n<ul>\r\n \t<li>Calculate a sample mean by hand<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the next preview assignment and in the next class, you will need to interpret features of a dotplot, use a random number generator to select a random sample from a finite population, and calculate the arithmetic mean. In this activity, you will become familiar with the data analysis tools that will be used throughout this course. You can access these tools on any smart device, including a phone.\r\n\r\nSome new vocabulary will appear in this section of course material. These are terms you'll discuss in greater terms later, that you'll use throughout the course, and that you may have seen before. As you work through this assignment, try to draw the statistical meaning of the words\u00a0<em>random<\/em> and\u00a0<em>sample<\/em> as they are used in context.\r\n\r\nThe two tools in this activity are the\u00a0<em>Describing and Exploring Quantitative Data<\/em> tool at\u00a0 <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a> and the\u00a0Generate Random Numbers tool at\r\n<a href=\"https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/\">https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/<\/a>. They'll also be linked below as you need them.\r\n\r\nWork in pairs during this activity if possible, in close proximity so that you can share and compare the outputs from the tool. If more than one of you share a device to complete the activity, switch roles halfway through so everyone gets practice using the tools.\r\n<h2>Interpreting Dotplots<\/h2>\r\n<span style=\"background-color: #ffff99;\">[insert image of a generic dotplot with labels, arrows pointing to individual observations, horizontal axis]<\/span>\r\n\r\nA <strong>dotplot<\/strong> is a graphical display of the distribution of a quantitative variable. It shows the variable\u2019s possible values and the frequency of each value. In this corequisite support activity, you will use technology to generate a dotplot and then use the dotplot to describe the features of the distribution. You will explore other ways of visualizing a quantitative variable in <em>Forming Connections [3C]<\/em>.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nGo to the Describing and Exploring Quantitative Data tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.\r\n\r\nStep 1) Select the Single Group tab.\r\n\r\nStep 2) Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.\r\n\r\nStep 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Cereal Sodium Content<\/strong>.\r\n\r\nStep 4) Under <strong>Choose Type of Plot<\/strong>, uncheck <strong>Histogram<\/strong> and <strong>Boxplot<\/strong> and check <strong>Dotplot<\/strong>. Then adjust the Dot size to 0.5 and the Bin width to 10.\r\n\r\nUse the dotplot displayed in the tool to answer the following questions.\r\n\r\n&nbsp;\r\n\r\nPart A: Which type of variable is cereal sodium content?\r\n\r\n[reveal-answer q=\"182576\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"182576\"]Is it categorical or quantitative?[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart B: Describe the typical value of cereal sodium content.\r\n\r\n[reveal-answer q=\"907818\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"907818\"]Look for a clump of dots on the graph clustered near a value.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart C: How many observations of cereal sodium content are less than 100 milligrams (mg)? Approximately what are the values of these observations?\r\n\r\n[reveal-answer q=\"109637\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"109637\"]Look for dots on the graph that are to the left of [latex]100[\/latex] on the horizontal axis.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart D: How many observations of cereal sodium content are between 200 and 300 mg (including 200 and 300)?\r\n\r\n[reveal-answer q=\"164496\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"164496\"]Locate 200 and 300 on the graph.\u00a0What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nYou'll be using the tools frequently throughout this course, and detailed instructions will be provided for each of the first few times you do, so don't worry if it doesn't yet feel comfortable.\r\n\r\nLet's turn our focus now to another tool you'll need to use soon, the random number generator.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Goals<\/h3>\n<p>In this support activity you\u2019ll become familiar with the following:<\/p>\n<ul>\n<li>Use technology to create a dotplot from a dataset.<\/li>\n<li>Answer questions about a variable using a dotplot.<\/li>\n<li>Use a random number generator to select a random sample.<\/li>\n<li>Anticipate sample-to-sample variability.<\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li>Calculate a sample mean by hand<\/li>\n<\/ul>\n<\/div>\n<p>In the next preview assignment and in the next class, you will need to interpret features of a dotplot, use a random number generator to select a random sample from a finite population, and calculate the arithmetic mean. In this activity, you will become familiar with the data analysis tools that will be used throughout this course. You can access these tools on any smart device, including a phone.<\/p>\n<p>Some new vocabulary will appear in this section of course material. These are terms you&#8217;ll discuss in greater terms later, that you&#8217;ll use throughout the course, and that you may have seen before. As you work through this assignment, try to draw the statistical meaning of the words\u00a0<em>random<\/em> and\u00a0<em>sample<\/em> as they are used in context.<\/p>\n<p>The two tools in this activity are the\u00a0<em>Describing and Exploring Quantitative Data<\/em> tool at\u00a0 <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a> and the\u00a0Generate Random Numbers tool at<br \/>\n<a href=\"https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/\">https:\/\/dcmathpathways.shinyapps.io\/RandomNumbers\/<\/a>. They&#8217;ll also be linked below as you need them.<\/p>\n<p>Work in pairs during this activity if possible, in close proximity so that you can share and compare the outputs from the tool. If more than one of you share a device to complete the activity, switch roles halfway through so everyone gets practice using the tools.<\/p>\n<h2>Interpreting Dotplots<\/h2>\n<p><span style=\"background-color: #ffff99;\">[insert image of a generic dotplot with labels, arrows pointing to individual observations, horizontal axis]<\/span><\/p>\n<p>A <strong>dotplot<\/strong> is a graphical display of the distribution of a quantitative variable. It shows the variable\u2019s possible values and the frequency of each value. In this corequisite support activity, you will use technology to generate a dotplot and then use the dotplot to describe the features of the distribution. You will explore other ways of visualizing a quantitative variable in <em>Forming Connections [3C]<\/em>.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>Go to the Describing and Exploring Quantitative Data tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.<\/p>\n<p>Step 1) Select the Single Group tab.<\/p>\n<p>Step 2) Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\n<p>Step 3) Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Cereal Sodium Content<\/strong>.<\/p>\n<p>Step 4) Under <strong>Choose Type of Plot<\/strong>, uncheck <strong>Histogram<\/strong> and <strong>Boxplot<\/strong> and check <strong>Dotplot<\/strong>. Then adjust the Dot size to 0.5 and the Bin width to 10.<\/p>\n<p>Use the dotplot displayed in the tool to answer the following questions.<\/p>\n<p>&nbsp;<\/p>\n<p>Part A: Which type of variable is cereal sodium content?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q182576\">Hint<\/span><\/p>\n<div id=\"q182576\" class=\"hidden-answer\" style=\"display: none\">Is it categorical or quantitative?<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part B: Describe the typical value of cereal sodium content.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q907818\">Hint<\/span><\/p>\n<div id=\"q907818\" class=\"hidden-answer\" style=\"display: none\">Look for a clump of dots on the graph clustered near a value.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part C: How many observations of cereal sodium content are less than 100 milligrams (mg)? Approximately what are the values of these observations?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q109637\">Hint<\/span><\/p>\n<div id=\"q109637\" class=\"hidden-answer\" style=\"display: none\">Look for dots on the graph that are to the left of [latex]100[\/latex] on the horizontal axis.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part D: How many observations of cereal sodium content are between 200 and 300 mg (including 200 and 300)?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q164496\">Hint<\/span><\/p>\n<div id=\"q164496\" class=\"hidden-answer\" style=\"display: none\">Locate 200 and 300 on the graph.\u00a0What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<p>You&#8217;ll be using the tools frequently throughout this course, and detailed instructions will be provided for each of the first few times you do, so don&#8217;t worry if it doesn&#8217;t yet feel comfortable.<\/p>\n<p>Let&#8217;s turn our focus now to another tool you&#8217;ll need to use soon, the random number generator.<\/p>\n","protected":false},"author":17533,"menu_order":2,"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-241","chapter","type-chapter","status-publish","hentry"],"part":158,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/241\/revisions"}],"predecessor-version":[{"id":254,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/241\/revisions\/254"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/parts\/158"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/241\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/media?parent=241"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapter-type?post=241"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/contributor?post=241"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/license?post=241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}