{"id":5821,"date":"2021-02-22T17:13:29","date_gmt":"2021-02-22T17:13:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/?post_type=chapter&#038;p=5821"},"modified":"2022-01-07T00:47:29","modified_gmt":"2022-01-07T00:47:29","slug":"4-18-margin-of-error-and-confidence-intervals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/4-18-margin-of-error-and-confidence-intervals\/","title":{"raw":"4.18 Margin of Error and Confidence Intervals","rendered":"4.18 Margin of Error and Confidence Intervals"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Introduction to Confidence Intervals<\/li>\r\n \t<li>Margin of Error<\/li>\r\n<\/ul>\r\n<\/div>\r\nSuppose you were trying to determine the mean rent of a two-bedroom apartment in your town. You might look in the classified section of the newspaper, write down several rents listed, and average them together. You would have obtained a point estimate of the true mean. If you are trying to determine the percentage of times you make a basket when shooting a basketball, you might count the number of shots you make and divide that by the number of shots you attempted. In this case, you would have obtained a point estimate for the true proportion.\r\n\r\nWe use sample data to make generalizations about an unknown population. This part of statistics is called\u00a0inferential statistics.\u00a0The sample data help us to make an estimate of a population\u00a0parameter. We realize that the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals.\r\n\r\nA\u00a0confidence interval\u00a0is another type of estimate but, instead of being just one number like the sample mean and sample standard deviation, it is an interval of numbers. The interval of numbers is a range of values calculated from a given set of sample data. The confidence interval is likely to include an unknown population parameter.\r\n\r\nRemember that a confidence interval is created for an unknown population parameter like the population mean,\u00a0\u03bc. Confidence intervals for some parameters have the form:\r\n\r\n(point estimate \u2013 margin of error, point estimate +\u00a0margin of error)\r\n\r\nWhen you read newspapers and journals, some reports will use the phrase \u201cmargin of error.\u201d Other reports will not use that phrase, but include a confidence interval as the point estimate plus or minus the margin of error. These are two ways of expressing the same concept.\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>This is the end of the book. Close this tab.<\/strong><\/span><\/p>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Introduction to Confidence Intervals<\/li>\n<li>Margin of Error<\/li>\n<\/ul>\n<\/div>\n<p>Suppose you were trying to determine the mean rent of a two-bedroom apartment in your town. You might look in the classified section of the newspaper, write down several rents listed, and average them together. You would have obtained a point estimate of the true mean. If you are trying to determine the percentage of times you make a basket when shooting a basketball, you might count the number of shots you make and divide that by the number of shots you attempted. In this case, you would have obtained a point estimate for the true proportion.<\/p>\n<p>We use sample data to make generalizations about an unknown population. This part of statistics is called\u00a0inferential statistics.\u00a0The sample data help us to make an estimate of a population\u00a0parameter. We realize that the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals.<\/p>\n<p>A\u00a0confidence interval\u00a0is another type of estimate but, instead of being just one number like the sample mean and sample standard deviation, it is an interval of numbers. The interval of numbers is a range of values calculated from a given set of sample data. The confidence interval is likely to include an unknown population parameter.<\/p>\n<p>Remember that a confidence interval is created for an unknown population parameter like the population mean,\u00a0\u03bc. Confidence intervals for some parameters have the form:<\/p>\n<p>(point estimate \u2013 margin of error, point estimate +\u00a0margin of error)<\/p>\n<p>When you read newspapers and journals, some reports will use the phrase \u201cmargin of error.\u201d Other reports will not use that phrase, but include a confidence interval as the point estimate plus or minus the margin of error. These are two ways of expressing the same concept.<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>This is the end of the book. Close this tab.<\/strong><\/span><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-5821\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">Lumen Learning authored content<\/div><ul class=\"citation-list\"><li>Introduction to Statistics - Lumen Learning Contributed bytDeborah Hur (Lumen Learning) Levelt Statistics Primary textbooktIntroductory Statistics, OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":383311,"menu_order":24,"template":"","meta":{"_candela_citation":"[{\"type\":\"lumen\",\"description\":\"Introduction to Statistics - Lumen Learning Contributed bytDeborah Hur (Lumen Learning) Levelt Statistics Primary textbooktIntroductory Statistics, OpenStax\",\"author\":\"\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5821","chapter","type-chapter","status-publish","hentry"],"part":329,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5821","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/users\/383311"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5821\/revisions"}],"predecessor-version":[{"id":7043,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5821\/revisions\/7043"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/parts\/329"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5821\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/media?parent=5821"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapter-type?post=5821"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/contributor?post=5821"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/license?post=5821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}