{"id":1139,"date":"2023-06-22T01:56:41","date_gmt":"2023-06-22T01:56:41","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/inference-basics-dig-deeper\/"},"modified":"2024-01-03T21:38:47","modified_gmt":"2024-01-03T21:38:47","slug":"inference-basics-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/inference-basics-dig-deeper\/","title":{"raw":"Inference Basics: Fresh Take","rendered":"Inference Basics: Fresh Take"},"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<section class=\"textbox keyTakeaway\">\r\n<h3>parameters &amp; statistics<\/h3>\r\n<p>We call the characteristic values of a sample <strong>statistics<\/strong>.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Characteristic values of a population are called\u00a0<strong>parameters<\/strong>.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Remember:<\/p>\r\n<ul>\r\n\t<li>A\u00a0<strong>s<\/strong>tatistic describes a characteristic of a\u00a0<strong>s<\/strong>ample.<\/li>\r\n\t<li>A\u00a0<strong>p<\/strong>arameter describes a characteristic of a\u00a0<strong>p<\/strong>opulation.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Consider the following statistical question: \u201cWhat is the average amount of money spent on textbooks per semester by full-time students in the three Arizona public universities?\u201d<\/p>\r\n<p>We cannot interview every full-time student in all of the three Arizona public universities because it would take too much time and cost too much money. We therefore carefully select a sample of full-time students from all three Arizona public universities to represent the population of all full-time students. Then we collect data from the sample to estimate the average amount spent on textbooks.<\/p>\r\n<p>A well-stated research question contains information about:<\/p>\r\n<ul>\r\n\t<li>The population: Full-time students from all three Arizona public universities.<\/li>\r\n\t<li>The information we will collect from each individual in the sample. We call this the\u00a0<strong>variable<\/strong>. The variable is what we plan to measure\u00a0 and is often represented by <em>[latex]X[\/latex]:<\/em> In our case, this is the amount of money spent on textbooks per semester.<\/li>\r\n\t<li>A numerical characteristic about the population related to this variable: The average amount of money spent on textbooks per semester.<\/li>\r\n<\/ul>\r\n<p>A numerical characteristic about a population is called a\u00a0<strong>parameter<\/strong>. In the example above we are interested in the average, or mean, amount of money all students spent on textbooks per semester.<\/p>\r\n<p>We use information from the sample to estimate the population mean. A numerical characteristic of a sample is called a\u00a0<strong>sample statistic<\/strong>.<\/p>\r\n<p>Another research question might be whether the majority of students qualify for federal student loans.<\/p>\r\n<ul>\r\n\t<li>The population: Full-time students from all three Arizona public university.<\/li>\r\n\t<li>The information we will collect from each individual in the sample is the\u00a0<strong>variable:<\/strong> Whether or not each student in the sample qualifies for federal student loans.<\/li>\r\n\t<li>The related population's numerical characteristic: The proportion of all students from all three Arizona public universities that qualify for student loans<\/li>\r\n<\/ul>\r\n<p>The parameter is the population proportion and the sample statistic is the sample proportion.<\/p>\r\n<p>If [latex]3[\/latex] out of [latex]5[\/latex] people in our sample agree with a statement, this corresponds to the sample proportion [latex]\\hat{p}=\\frac{3}{5}=0.6[\/latex].<\/p>\r\n<section class=\"textbox proTip\">If information includes all members of the population, the information refers to a population parameter. The word \u201cevery\u201d or \u201ceach\u201d or \"all\" in a statement can be a clue that an entire population has been included.<\/section>\r\n<section class=\"textbox proTip\">A numerical characteristic refers to a sample statistic if only a portion of the population has been included. Information likely refers to a sample if a statement refers to a relatively small sample of a large population.\u00a0<\/section>\r\n<section class=\"textbox example\">Determine whether the number refers to a population parameter or a sample statistic.\r\n\r\n<ol>\r\n\t<li>[latex]78\\%[\/latex] of [latex]50[\/latex] athletes at a large university said they were happy they chose to continue competing at the collegiate level.<\/li>\r\n\t<li>[latex]706[\/latex] of the [latex]2,223[\/latex] passengers on the Titanic survived.<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"634009\"]Show answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"634009\"]<\/p>\r\n<ol>\r\n\t<li>Since a large university likely has many more than [latex]50[\/latex] athletes, and the statement refers to a survey, [latex]78\\%[\/latex] refers to a sample statistic, [latex]\\hat{p}[\/latex].<\/li>\r\n\t<li>The statement refers to all passengers on the Titanic, so [latex]706[\/latex] out of [latex]2,223[\/latex], or [latex]31.8\\%[\/latex], refers to a population proportion, [latex]p[\/latex].<\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>","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<section class=\"textbox keyTakeaway\">\n<h3>parameters &amp; statistics<\/h3>\n<p>We call the characteristic values of a sample <strong>statistics<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>Characteristic values of a population are called\u00a0<strong>parameters<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>Remember:<\/p>\n<ul>\n<li>A\u00a0<strong>s<\/strong>tatistic describes a characteristic of a\u00a0<strong>s<\/strong>ample.<\/li>\n<li>A\u00a0<strong>p<\/strong>arameter describes a characteristic of a\u00a0<strong>p<\/strong>opulation.<\/li>\n<\/ul>\n<\/section>\n<p>Consider the following statistical question: \u201cWhat is the average amount of money spent on textbooks per semester by full-time students in the three Arizona public universities?\u201d<\/p>\n<p>We cannot interview every full-time student in all of the three Arizona public universities because it would take too much time and cost too much money. We therefore carefully select a sample of full-time students from all three Arizona public universities to represent the population of all full-time students. Then we collect data from the sample to estimate the average amount spent on textbooks.<\/p>\n<p>A well-stated research question contains information about:<\/p>\n<ul>\n<li>The population: Full-time students from all three Arizona public universities.<\/li>\n<li>The information we will collect from each individual in the sample. We call this the\u00a0<strong>variable<\/strong>. The variable is what we plan to measure\u00a0 and is often represented by <em>[latex]X[\/latex]:<\/em> In our case, this is the amount of money spent on textbooks per semester.<\/li>\n<li>A numerical characteristic about the population related to this variable: The average amount of money spent on textbooks per semester.<\/li>\n<\/ul>\n<p>A numerical characteristic about a population is called a\u00a0<strong>parameter<\/strong>. In the example above we are interested in the average, or mean, amount of money all students spent on textbooks per semester.<\/p>\n<p>We use information from the sample to estimate the population mean. A numerical characteristic of a sample is called a\u00a0<strong>sample statistic<\/strong>.<\/p>\n<p>Another research question might be whether the majority of students qualify for federal student loans.<\/p>\n<ul>\n<li>The population: Full-time students from all three Arizona public university.<\/li>\n<li>The information we will collect from each individual in the sample is the\u00a0<strong>variable:<\/strong> Whether or not each student in the sample qualifies for federal student loans.<\/li>\n<li>The related population&#8217;s numerical characteristic: The proportion of all students from all three Arizona public universities that qualify for student loans<\/li>\n<\/ul>\n<p>The parameter is the population proportion and the sample statistic is the sample proportion.<\/p>\n<p>If [latex]3[\/latex] out of [latex]5[\/latex] people in our sample agree with a statement, this corresponds to the sample proportion [latex]\\hat{p}=\\frac{3}{5}=0.6[\/latex].<\/p>\n<section class=\"textbox proTip\">If information includes all members of the population, the information refers to a population parameter. The word \u201cevery\u201d or \u201ceach\u201d or &#8220;all&#8221; in a statement can be a clue that an entire population has been included.<\/section>\n<section class=\"textbox proTip\">A numerical characteristic refers to a sample statistic if only a portion of the population has been included. Information likely refers to a sample if a statement refers to a relatively small sample of a large population.\u00a0<\/section>\n<section class=\"textbox example\">Determine whether the number refers to a population parameter or a sample statistic.<\/p>\n<ol>\n<li>[latex]78\\%[\/latex] of [latex]50[\/latex] athletes at a large university said they were happy they chose to continue competing at the collegiate level.<\/li>\n<li>[latex]706[\/latex] of the [latex]2,223[\/latex] passengers on the Titanic survived.<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q634009\">Show answer<\/button><\/p>\n<div id=\"q634009\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Since a large university likely has many more than [latex]50[\/latex] athletes, and the statement refers to a survey, [latex]78\\%[\/latex] refers to a sample statistic, [latex]\\hat{p}[\/latex].<\/li>\n<li>The statement refers to all passengers on the Titanic, so [latex]706[\/latex] out of [latex]2,223[\/latex], or [latex]31.8\\%[\/latex], refers to a population proportion, [latex]p[\/latex].<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"author":8,"menu_order":13,"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":"fresh_take","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\/1139"}],"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":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1139\/revisions"}],"predecessor-version":[{"id":4742,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1139\/revisions\/4742"}],"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\/1139\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1139"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1139"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1139"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}