{"id":1153,"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-2\/"},"modified":"2025-05-16T02:56:26","modified_gmt":"2025-05-16T02:56:26","slug":"sampling-variability-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-variability-learn-it-2\/","title":{"raw":"Sampling Variability: Learn It 2","rendered":"Sampling Variability: Learn It 2"},"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<h2><strong>The Normal Condition for a Sampling Distribution of Sample Proportions<\/strong><\/h2>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>Central Limit Theorem<\/h3>\r\n<p>The <strong>Central Limit Theorem<\/strong> states that, as the sample size gets larger, the distribution of the sample proportion will become closer to a normal distribution.<\/p>\r\n<\/section>\r\n<p>In order to estimate probabilities from our sampling distribution, we need the distribution to be approximately normal.\u00a0<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>The Normal Condition for Proportions<\/h3>\r\n<p>Given a population proportion, [latex]p[\/latex] and a sample size [latex]n[\/latex], if [latex]np\\ge10[\/latex] and [latex]n(1-p)\\ge10[\/latex] then we assume that the sampling distribution of the sample proportion is approximately normal.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]15547[\/ohm2_question]<\/p>\r\n<\/section>\r\n<ul>\r\n\t<li>Proportions from random samples approximate the population proportion, [latex]p[\/latex], so sample proportions average out to the population proportion.<\/li>\r\n\t<li>Larger random samples better approximate the population proportion, so large samples have sample proportions closer to [latex]p[\/latex]. In other words, a sampling distribution for large samples has less variability.<\/li>\r\n\t<li>The distribution of sample proportions appears normal when the sample size is sufficiently large<\/li>\r\n<\/ul>","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<h2><strong>The Normal Condition for a Sampling Distribution of Sample Proportions<\/strong><\/h2>\n<section class=\"textbox keyTakeaway\">\n<h3>Central Limit Theorem<\/h3>\n<p>The <strong>Central Limit Theorem<\/strong> states that, as the sample size gets larger, the distribution of the sample proportion will become closer to a normal distribution.<\/p>\n<\/section>\n<p>In order to estimate probabilities from our sampling distribution, we need the distribution to be approximately normal.\u00a0<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>The Normal Condition for Proportions<\/h3>\n<p>Given a population proportion, [latex]p[\/latex] and a sample size [latex]n[\/latex], if [latex]np\\ge10[\/latex] and [latex]n(1-p)\\ge10[\/latex] then we assume that the sampling distribution of the sample proportion is approximately normal.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm15547\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=15547&theme=lumen&iframe_resize_id=ohm15547&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<ul>\n<li>Proportions from random samples approximate the population proportion, [latex]p[\/latex], so sample proportions average out to the population proportion.<\/li>\n<li>Larger random samples better approximate the population proportion, so large samples have sample proportions closer to [latex]p[\/latex]. In other words, a sampling distribution for large samples has less variability.<\/li>\n<li>The distribution of sample proportions appears normal when the sample size is sufficiently large<\/li>\n<\/ul>\n","protected":false},"author":8,"menu_order":21,"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\/1153"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1153\/revisions"}],"predecessor-version":[{"id":6710,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1153\/revisions\/6710"}],"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\/1153\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1153"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1153"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1153"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}