{"id":2458,"date":"2019-08-27T17:37:00","date_gmt":"2019-08-27T17:37:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=2458"},"modified":"2026-02-10T08:54:44","modified_gmt":"2026-02-10T08:54:44","slug":"one-tailed-vs-two-tailed-hypothesis-testing","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/one-tailed-vs-two-tailed-hypothesis-testing\/","title":{"rendered":"One-tailed vs. Two-tailed Hypothesis Testing"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Hypothesis Testing (2025 Level I CFA\u00ae Exam \u2013 Quantitative Methods \u2013 Module 6)\",\n  \"description\": \"This CFA Level 1 module dives into hypothesis testing, one of the most critical yet challenging topics in quantitative methods. Learn the foundational concepts of null and alternative hypotheses, test statistics, p-values, and significance levels through engaging, real-world examples like analyzing investment objectives and testing financial claims. Topics include Type I and Type II errors, parametric vs. non-parametric tests, and contingency tables. Master key testing techniques such as t-tests, z-tests, and chi-square tests, ensuring a thorough grasp of hypothesis testing for financial decision-making and CFA exam success.\",\n  \"uploadDate\": \"2021-11-18T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/twTTWMuEGx8\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=twTTWMuEGx8\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/twTTWMuEGx8\",\n  \"duration\": \"PT58M47S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-167.jpg\",\n  \"caption\": \"Image showing the one-tailed test.\",\n  \"width\": 1473,\n  \"height\": 912,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-168.jpg\",\n  \"caption\": \"Image showing the two-tailed test.\",\n  \"width\": 1473,\n  \"height\": 900,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/twTTWMuEGx8?si=JivMQ-iEq16cLRTy\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<p>A one-tailed test (one-sided test) is a statistical test that considers a change in only one direction. In such a test, the alternative hypothesis either has a &lt; (less than sign) or &gt; (greater than sign), i.e., we consider either an increase or reduction, but not both.<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Breaking Down a One-tailed Test<\/strong><\/h2>\n\n\n\n<p>A one-tailed test directs all the significance level (\u03b1) to the testing of statistical significance in one direction. In other words, we aim at testing the possibility of a change in one direction and completely disregard the possibility of a change in the other direction.<\/p>\n\n\n\n<p>If we have a 5% significance level, we shall allot 0.05 of the total area in one tail of the distribution of our test statistic.<\/p>\n\n\n\n<!-- TOP CTA \u2013 Full Width Outline Button -->\n<div style=\"margin:24px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:block;\n       width:100%;\n       padding:14px 0;\n       border:2px solid #3b6fd8;\n       border-radius:50px;\n       font-size:18px;\n       font-weight:500;\n       text-align:center;\n       text-decoration:none;\n       color:#3b6fd8;\n       background-color:#f4f6f9;\n       box-sizing:border-box;\n     \">\n     Practice hypothesis testing questions with free trial access.\n  <\/a>\n<\/div>\n\n\n\n<h4><strong>Examples: Hypothesis Testing<\/strong><\/h4>\n<p>Let us assume that we are using the standardized normal distribution to test the hypothesis that the population mean is equal to a given value X.\u00a0 Further, let us assume that we are using data from a sample drawn from the population of interest. Our null hypothesis can be expressed as:<\/p>\n<p>$$ H_0: \\ \\mu = X $$<\/p>\n<p>If our test is one-tailed, the alternative hypothesis will test if the mean is either significantly greater than X or significantly less than X, but NOT both.<\/p>\n<p><strong>Case 1: At the 95% Confidence Level<\/strong><\/p>\n<p>$$ H_1: \\ \\mu &lt; X $$<\/p>\n<p>The mean is significantly less than X if the test statistic is in the bottom 5% of the probability distribution. This bottom area is known as the critical region (rejection region). We will reject the null hypothesis if the test statistic is less than -1.645.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-17050 size-full\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-167.jpg\" alt=\"Image showing the one-tailed test\" width=\"1473\" height=\"912\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-167.jpg 1473w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-167-300x186.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-167-768x476.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-167-1024x634.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-167-400x248.jpg 400w\" sizes=\"auto, (max-width: 1473px) 100vw, 1473px\" \/><\/p>\n<p><strong>Case 2: Still at the 95% Confidence Level<\/strong><\/p>\n<p>$$ H_1: \\\u00a0 \\mu &gt; X $$<\/p>\n<p>We would reject the null hypothesis only if the test statistic is greater than the upper 5% point of the distribution. In other words, we would reject H<sub>0<\/sub> if the test statistic is greater than 1.645.<\/p>\n<h2><strong>A Two-tailed Test<\/strong><\/h2>\n<p>A two-tailed test considers the possibility of a change in either direction. It looks for a statistical relationship in both the positive and negative directions of a distribution. Therefore, it allows half the value of \u03b1 to test statistical significance in one direction and the other half to test the same in the opposite direction. A two-tailed test may have the following set of hypotheses:<\/p>\n<p>$$ H_0: \\mu = X $$<\/p>\n<p>$$ H_1: \\mu \\neq X $$<\/p>\n<p>Refer to our earlier example. If we were to carry out a two-tailed test, we would reject H<sub>0 <\/sub>if the test statistic turned out to be less than the lower 2.5% point or greater than the upper 2.5% point of the normal distribution.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-17052 size-full\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-168.jpg\" alt=\"Image showing the two-tailed test\" width=\"1473\" height=\"900\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-168.jpg 1473w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-168-300x183.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-168-768x469.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-168-1024x626.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-168-400x244.jpg 400w\" sizes=\"auto, (max-width: 1473px) 100vw, 1473px\" \/><\/p>\n<div class=\"notes_inv\"><hr \/><\/div>\n\n\n<!-- BOTTOM CTA \u2013 Refined Version -->\n<div style=\"text-align:center; background-color:#f4f6f9; padding:35px 20px; border-radius:12px; margin-top:40px;\">\n\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:inline-block;\n       padding:14px 34px;\n       background-color:#3b6fd8;\n       color:#ffffff;\n       border-radius:50px;\n       font-size:16px;\n       font-weight:600;\n       text-decoration:none;\n       margin-bottom:18px;\n     \">\n     Start Free Trial\n  <\/a>\n\n  <p style=\"max-width:700px; margin:0 auto; font-size:16px; line-height:1.6; color:#333;\">\n    Improve your CFA Level I statistics skills with exam-style one tailed and two tailed hypothesis testing problems, detailed explanations, and timed practice designed to sharpen decision making under exam conditions.\n  <\/p>\n\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>A one-tailed test (one-sided test) is a statistical test that considers a change in only one direction. In such a test, the alternative hypothesis either has a &lt; (less than sign) or &gt; (greater than sign), i.e., we consider either&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-2458","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>One-tailed Vs Two-tailed Tests I CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Learn what a one-tailed hypothesis is and how it differs from a two-tailed hypothesis. 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