{"id":115,"date":"2018-03-27T20:36:00","date_gmt":"2018-03-27T18:36:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/27\/hypothesis-testing-question-20-run-test-suppose-we-flib-a-coin\/"},"modified":"2026-07-13T00:29:42","modified_gmt":"2026-07-12T22:29:42","slug":"hypothesis-testing-question-20-run-test-suppose-we-flib-a-coin","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-question-20-run-test-suppose-we-flib-a-coin\/","title":{"rendered":"Hypothesis Testing Question 20 \u2013 Run Test( Suppose we flip a coin\u2026)"},"content":{"rendered":"<p><!-- ktg-updated-banner --><\/p>\n<div class=\"ktg-updated-banner\" style=\"margin:1em 0;padding:0.75em 1em;background:#eff6ff;border-left:4px solid #3b82f6;border-radius:4px;\">\n<p><strong>Updated July 12, 2026:<\/strong> Refreshed for SEO \u2014 Question 20 (Run test). Part of the <a href=\"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-solved-examplesquestions-and-solutions\/\">20 hypothesis testing solved examples<\/a> series.<\/p>\n<\/div>\n<nav class=\"ktg-question-nav\" aria-label=\"Hypothesis testing question navigation\" style=\"margin:1em 0;padding:0.75em 1em;background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;display:flex;flex-wrap:wrap;gap:1em;justify-content:space-between;\"><a href=\"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-question-19-run-test-trees-were-planted\/\">\u2190 Question 19<\/a> \u00b7 <a href=\"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-solved-examplesquestions-and-solutions\/\">All 20 questions<\/a><\/nav>\n<p><span style=\"color: #cc0000;\"><b>Question 20<\/b><\/span><br \/>\nSuppose we flip a coin n = 15 times and come up with the following arrangements<\/p>\n<p>H T T T H H T T T T H H T H H<\/p>\n<p>(H = head, T = tail)<\/p>\n<p>Test at the alpha = 0.05 significance level whether this arrangement may be regarded as random.<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #274e13;\"><b>Solution Steps<\/b><\/span><br \/>\n<b>Step 1:<\/b> State the null and alternate hypothesis<br \/>\nH<sub>0<\/sub>: Arrangement is random<br \/>\nH<sub>1<\/sub>: Arrangement is not random<\/p>\n<p>&nbsp;<\/p>\n<p><b>Step 2<\/b>: Calculate the Test Statistic (Number of Runs)<br \/>\nNormally you separate each of the runs so that you would be able to count them.<\/p>\n<p>H\u00a0 <span style=\"color: #cc0000;\">TTT\u00a0 <\/span>HH\u00a0 <span style=\"color: #cc0000;\">TTTT\u00a0 <\/span>HH\u00a0 <span style=\"color: #cc0000;\">T\u00a0<\/span> HH<\/p>\n<p>Number of runs is given by r = 7<br \/>\nNumber of H, n<sub>1<\/sub> = 7<br \/>\nNumber of T, n<sub>2<\/sub> =8<\/p>\n<p>Test Statistic = 7 (number of runs)<\/p>\n<p>&nbsp;<\/p>\n<p><b>Step 3: <\/b>Lookup Critical values in table of runs tests<br \/>\nAt\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"mwe-math-fallback-image-inline\" style=\"-webkit-text-stroke-width: 0px; background-color: white; border: 0px; color: #222222; display: inline-block; font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; height: 1.676ex; letter-spacing: normal; margin: 0px -0.299ex 0px 0px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-indent: 0px; text-transform: none; vertical-align: -0.338ex; white-space: normal; widows: 2; width: 0.995ex; word-spacing: 0px;\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f4bd2f8c9241ab34af72babb5f87c90a2521338e\" alt=\"varepsilon !\" width=\"373\" height=\"640\" \/>\u00a0 = 0.05 significance, n<sub>1<\/sub> = 7, n<sub>2<\/sub> =8<br \/>\nUpper critical value =\u00a0 4<br \/>\nLower critical value = 13<\/p>\n<p>&nbsp;<\/p>\n<p><b>Step 4: <\/b>Make Your Decision<br \/>\nSince r = 10 which is between 4 and 13, we accept the null hypothesis (we fail to reject it)<\/p>\n<p>&nbsp;<\/p>\n<p><b>Step 5:<\/b> Draw a Conclusion<br \/>\nThere are not enough evidence to reject the claim hat the pattern of occurrence of heads and tails is determined by a random process<\/p>\n<p><ins style=\"display: block; text-align: center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-7041870931346451\" data-ad-slot=\"4209786523\"><\/ins><br \/>\n<ins style=\"display: block; text-align: center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-7041870931346451\" data-ad-slot=\"4209786523\"><\/ins><\/p>\n<section class=\"ktg-related\" style=\"margin:2em 0;padding:1em 1.25em;background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;\">\n<h2>Related<\/h2>\n<ul>\n<li><a href=\"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-solved-examplesquestions-and-solutions\/\">All hypothesis testing solved examples<\/a><\/li>\n<li><strong>Test type:<\/strong> Run test<\/li>\n<li><a href=\"https:\/\/kindsonthegenius.com\/blog\/what-is-run-test-in-statistics-a-simple-explanation-with-step-by-step-examples\/\">Method tutorial<\/a><\/li>\n<li><a href=\"https:\/\/kindsonthegenius.com\/blog\/statistics-tutorial-3-hypothesis-testing\/\">Hypothesis testing basics<\/a><\/li>\n<\/ul>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>Updated July 12, 2026: Refreshed for SEO \u2014 Question 20 (Run test). Part of the 20 hypothesis testing solved examples series. \u2190 Question 19 \u00b7 &hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"pagelayer_contact_templates":[],"_pagelayer_content":"","footnotes":""},"categories":[223],"tags":[],"class_list":["post-115","post","type-post","status-publish","format-standard","hentry","category-hypothesis-testing"],"_links":{"self":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/115","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/comments?post=115"}],"version-history":[{"count":3,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/115\/revisions"}],"predecessor-version":[{"id":2237,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/115\/revisions\/2237"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=115"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=115"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}