{"id":1152,"date":"2023-06-22T01:56:53","date_gmt":"2023-06-22T01:56:53","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-variability-learn-it-1\/"},"modified":"2025-05-16T02:55:59","modified_gmt":"2025-05-16T02:55:59","slug":"sampling-variability-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-variability-learn-it-1\/","title":{"raw":"Sampling Variability: Learn It 1","rendered":"Sampling Variability: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for normal approximation of a sampling distribution of a sample proportion&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions for normal approximation of a sampling distribution of a sample proportion.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal distribution to calculate probabilities and percentiles from a sampling distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Use the normal distribution to calculate probabilities and percentiles from a sampling distribution.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal distribution to calculate probabilities and percentiles from a sampling distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Find the sample size needed for a sampling distribution to have a desired standard deviation.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>The center, spread, and shape of a sampling distribution of a sample proportion vary depending on the sample size, [latex]n[\/latex], and the population proportion, [latex]p[\/latex].<\/p>\r\n<p>Let's use the statistical tool to simulate sample proportions from samples of varying sizes, [latex]n[\/latex], from populations with varying proportions, [latex]p[\/latex].<\/p>\r\n<section class=\"textbox interact\">Make sure to:\r\n\r\n<ul>\r\n\t<li>Leave the default values for the population proportion ([latex]p[\/latex]) and the sample size ([latex]n[\/latex]).<\/li>\r\n\t<li>Select [latex]1,000[\/latex] and click <strong>Draw Samples<\/strong> to generate sample proportions from [latex]1,000[\/latex] random samples.<\/li>\r\n\t<li>Check the <strong>Show Normal Approximation<\/strong>\u00a0option box. This will overlay a normal distribution on the distribution of sample proportions, which will allow you to compare how closely the simulated distribution follows a normal distribution.<\/li>\r\n<\/ul>\r\n<p>The bottom plot in the tool, <strong>Sampling Distribution of Sample Proportion<\/strong>, now displays a plot of the distribution of these randomly generated sample proportions.<\/p>\r\n<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_prop\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_prop\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1601[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for normal approximation of a sampling distribution of a sample proportion&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions for normal approximation of a sampling distribution of a sample proportion.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal distribution to calculate probabilities and percentiles from a sampling distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Use the normal distribution to calculate probabilities and percentiles from a sampling distribution.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal distribution to calculate probabilities and percentiles from a sampling distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Find the sample size needed for a sampling distribution to have a desired standard deviation.<\/span><\/li>\n<\/ul>\n<\/section>\n<p>The center, spread, and shape of a sampling distribution of a sample proportion vary depending on the sample size, [latex]n[\/latex], and the population proportion, [latex]p[\/latex].<\/p>\n<p>Let&#8217;s use the statistical tool to simulate sample proportions from samples of varying sizes, [latex]n[\/latex], from populations with varying proportions, [latex]p[\/latex].<\/p>\n<section class=\"textbox interact\">Make sure to:<\/p>\n<ul>\n<li>Leave the default values for the population proportion ([latex]p[\/latex]) and the sample size ([latex]n[\/latex]).<\/li>\n<li>Select [latex]1,000[\/latex] and click <strong>Draw Samples<\/strong> to generate sample proportions from [latex]1,000[\/latex] random samples.<\/li>\n<li>Check the <strong>Show Normal Approximation<\/strong>\u00a0option box. This will overlay a normal distribution on the distribution of sample proportions, which will allow you to compare how closely the simulated distribution follows a normal distribution.<\/li>\n<\/ul>\n<p>The bottom plot in the tool, <strong>Sampling Distribution of Sample Proportion<\/strong>, now displays a plot of the distribution of these randomly generated sample proportions.<\/p>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_prop\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_prop\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1601\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1601&theme=lumen&iframe_resize_id=ohm1601&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":20,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1126,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1152"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":9,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1152\/revisions"}],"predecessor-version":[{"id":6709,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1152\/revisions\/6709"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1126"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1152\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1152"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1152"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1152"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}