{"id":2709,"date":"2021-11-12T13:39:55","date_gmt":"2021-11-12T13:39:55","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2709"},"modified":"2023-12-05T09:30:55","modified_gmt":"2023-12-05T09:30:55","slug":"putting-it-together-confidence-intervals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/putting-it-together-confidence-intervals\/","title":{"raw":"Putting It Together: Confidence Intervals","rendered":"Putting It Together: Confidence Intervals"},"content":{"raw":"<h2>Let\u2019s Summarize<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A confidence interval is formed by taking a single value (point estimate) and adding and subtracting an error bound (margin of error).<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The formula for creating a confidence interval for a mean is based on a normal distribution if the population standard deviation is known. If the population standard deviation is not known, then a <em>t<\/em>-distribution is used with degrees of freedom (df) equal to the sample size minus 1.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The formula for creating a confidence interval for a proportion is based on a normal distribution.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The size of the error bound is based on the confidence level, standard deviation (or standard error) and the sample size.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The confidence level refers to the long-run success rate of all possible confidence intervals from all possible random samples of a given sample size.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">For a given confidence level, intervals are narrower for larger sample sizes.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">For a given sample size, intervals are wider for larger confidence levels.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">When constructing a confidence interval for a proportion, the \u201cplus-four\u201d method of adding two additional successes and two additional failures can be used to produce more accurate confidence intervals.<\/li>\r\n<\/ul>","rendered":"<h2>Let\u2019s Summarize<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A confidence interval is formed by taking a single value (point estimate) and adding and subtracting an error bound (margin of error).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The formula for creating a confidence interval for a mean is based on a normal distribution if the population standard deviation is known. If the population standard deviation is not known, then a <em>t<\/em>-distribution is used with degrees of freedom (df) equal to the sample size minus 1.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The formula for creating a confidence interval for a proportion is based on a normal distribution.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The size of the error bound is based on the confidence level, standard deviation (or standard error) and the sample size.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The confidence level refers to the long-run success rate of all possible confidence intervals from all possible random samples of a given sample size.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">For a given confidence level, intervals are narrower for larger sample sizes.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">For a given sample size, intervals are wider for larger confidence levels.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">When constructing a confidence interval for a proportion, the \u201cplus-four\u201d method of adding two additional successes and two additional failures can be used to produce more accurate confidence intervals.<\/li>\n<\/ul>\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-2709\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/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":169134,"menu_order":21,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2709","chapter","type-chapter","status-publish","hentry"],"part":269,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2709","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2709\/revisions"}],"predecessor-version":[{"id":3786,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2709\/revisions\/3786"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/269"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2709\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2709"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2709"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2709"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}