{"id":117,"date":"2018-03-27T13:39:00","date_gmt":"2018-03-27T11:39:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/27\/hypothesis-testing-question-19-run-test-trees-were-planted\/"},"modified":"2026-07-13T00:29:31","modified_gmt":"2026-07-12T22:29:31","slug":"hypothesis-testing-question-19-run-test-trees-were-planted","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-question-19-run-test-trees-were-planted\/","title":{"rendered":"Hypothesis Testing Question 19 \u2013 Run Test ( Trees were planted\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 19 (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\/chi-square-test-for-independence-question-18-a-publisher-is-interested\/\">\u2190 Question 18<\/a> \u00b7 <a href=\"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-solved-examplesquestions-and-solutions\/\">All 20 questions<\/a> \u00b7 <a href=\"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-question-20-run-test-suppose-we-flib-a-coin\/\">Question 20 \u2192<\/a><\/nav>\n<div style=\"color: #555555; font-size: 18px; line-height: 30px; text-align: justify;\">\n<div style=\"font-family: 'segoe ui';\">\n<p><strong><span style=\"color: #cc0000;\">Question 19<\/span><\/strong><br \/>\nTrees planted along the road were checked for which ones are healthy(H) or deseased (D) and the following arrangement of the trees were obtained:<\/p>\n<p>H H H H D D D H H H H H H H D D H H D D D<\/p>\n<p>Test at the\u00a0 <span style=\"background-color: white; clip: rect(1px , 1px , 1px , 1px); color: #222222; display: none; font-family: sans-serif; font-size: 16.52px; font-style: normal; font-weight: 400; height: 1px; letter-spacing: normal; opacity: 0; overflow: hidden; position: absolute; text-indent: 0px; text-transform: none; white-space: normal; width: 1px; word-spacing: 0px;\">{displaystyle varepsilon !}<\/span><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 signnificance wether this arrangeemnt may be regarded as random<\/p>\n<p>&nbsp;<\/p>\n<p><strong><span style=\"color: #38761d;\">Solution Steps<\/span><\/strong><br \/>\n<strong>Stetp 1:<\/strong> State the null and alternate hypothesis<br \/>\nH0: Arrangement is random<br \/>\nH1: Arrangement is not random<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Step 2<\/strong>: Calculate the number of runs, H and D<\/p>\n<p><span style=\"color: #274e13;\">H H H H<\/span> <span style=\"color: red;\">D D D<\/span> <span style=\"color: #274e13;\">H H H H H H H <\/span><span style=\"color: #cc0000;\">D D <\/span><span style=\"color: #274e13;\">H H <\/span><span style=\"color: #cc0000;\">D D D D<\/span><\/p>\n<p>Number of runs is given by R = 6<br \/>\nNumber of H,  n<sub>1<\/sub>  = 13<br \/>\nNumber of D, n<sub>2<\/sub> = 9<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Step 3: <\/strong>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 signnificance, n<sub>1<\/> = 13, n<sub>2<\/sub> = 9<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Step 4: <\/strong>State your Conclusion<br \/>\nIn this case , since the absolute value calculated is less than the critical value, we reject the null hypothesis and conclude that the arrangement is not random<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Note about the Run Test<\/strong><br \/>\nThe Run Test (which is also the Wald-Wolfowitz runs test) is a non-parametric statistical test that tests the randomness of a hypothesis for a 2-valued sequence of data.<br \/>\nIt is used to test the hypothesis that the elements of the sequence are mutually independent<\/p>\n<\/div>\n<\/div>\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 19 (Run test). Part of the 20 hypothesis testing solved examples series. \u2190 Question 18 \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-117","post","type-post","status-publish","format-standard","hentry","category-hypothesis-testing"],"_links":{"self":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/117","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=117"}],"version-history":[{"count":4,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/117\/revisions"}],"predecessor-version":[{"id":2236,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/117\/revisions\/2236"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=117"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=117"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=117"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}