{"id":1137,"date":"2023-06-22T01:56:39","date_gmt":"2023-06-22T01:56:39","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/inference-basics-apply-it-2\/"},"modified":"2025-05-16T02:36:49","modified_gmt":"2025-05-16T02:36:49","slug":"inference-basics-apply-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/inference-basics-apply-it-2\/","title":{"raw":"Inference Basics: Learn It 2","rendered":"Inference Basics: 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;Describe a population and sample of interest&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;}\">Describe a population and sample of interest.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use technology to find sample statistics 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 technology to find sample statistics from a sampling distribution.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Inferential Statistics<\/h2>\r\n<section class=\"textbox proTip\">One of the goals of statistical inference is to draw a conclusion about a population on the basis of a random sample from the population.<\/section>\r\n<p>We need to understand how much random samples vary and how they relate to the population. Our ultimate goal is to create a probability model that describes the long-term behavior of sample measurements. We use this model to make inferences about the population.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6569[\/ohm2_question]<\/section>\r\n<h3>Sampling Distribution of a Statistic<\/h3>\r\n<p>Let\u2019s use this new vocabulary to rephrase what we already know at this point:<\/p>\r\n<ul>\r\n\t<li>When we make inferences, a parameter is typically not known because it is impossible or impractical to gather data from everyone in the population. (Note: In order to investigate how statistics relate to parameters, we used a known parameter in our example. This is the first step in creating a probability model. However, when we make inferences in real life, we use a statistic to draw a conclusion about an unknown parameter.)<\/li>\r\n\t<li>We make an inference about the population parameter on the basis of a sample statistic.<\/li>\r\n\t<li>Statistics from samples vary.<\/li>\r\n<\/ul>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>sampling distribution of a statistic<\/h3>\r\n<p>The <strong>sampling distribution<\/strong> of a statistic is a probability distribution that describes the long-term behavior of the statistic.<\/p>\r\n<\/section>\r\n<p>An approximate sampling distribution can be constructed from a large number of samples of size [latex]n[\/latex] from a given population. So, to create a probability model that describes the long-term behavior of the statistic, we can collect a few random samples to make a distribution of the sample statistic, and we can use technology to help us create such a distribution.<\/p>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Describe a population and sample of interest&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;}\">Describe a population and sample of interest.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use technology to find sample statistics 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 technology to find sample statistics from a sampling distribution.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Inferential Statistics<\/h2>\n<section class=\"textbox proTip\">One of the goals of statistical inference is to draw a conclusion about a population on the basis of a random sample from the population.<\/section>\n<p>We need to understand how much random samples vary and how they relate to the population. Our ultimate goal is to create a probability model that describes the long-term behavior of sample measurements. We use this model to make inferences about the population.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6569\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6569&theme=lumen&iframe_resize_id=ohm6569&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h3>Sampling Distribution of a Statistic<\/h3>\n<p>Let\u2019s use this new vocabulary to rephrase what we already know at this point:<\/p>\n<ul>\n<li>When we make inferences, a parameter is typically not known because it is impossible or impractical to gather data from everyone in the population. (Note: In order to investigate how statistics relate to parameters, we used a known parameter in our example. This is the first step in creating a probability model. However, when we make inferences in real life, we use a statistic to draw a conclusion about an unknown parameter.)<\/li>\n<li>We make an inference about the population parameter on the basis of a sample statistic.<\/li>\n<li>Statistics from samples vary.<\/li>\n<\/ul>\n<section class=\"textbox keyTakeaway\">\n<h3>sampling distribution of a statistic<\/h3>\n<p>The <strong>sampling distribution<\/strong> of a statistic is a probability distribution that describes the long-term behavior of the statistic.<\/p>\n<\/section>\n<p>An approximate sampling distribution can be constructed from a large number of samples of size [latex]n[\/latex] from a given population. So, to create a probability model that describes the long-term behavior of the statistic, we can collect a few random samples to make a distribution of the sample statistic, and we can use technology to help us create such a distribution.<\/p>\n","protected":false},"author":8,"menu_order":9,"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\/1137"}],"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\/1137\/revisions"}],"predecessor-version":[{"id":6703,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1137\/revisions\/6703"}],"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\/1137\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1137"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1137"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1137"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}