{"id":152,"date":"2018-03-06T13:37:00","date_gmt":"2018-03-06T12:37:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/06\/hypothesis-testing-problems-question-8an-automatic-cutter-machine\/"},"modified":"2026-07-13T00:27:26","modified_gmt":"2026-07-12T22:27:26","slug":"hypothesis-testing-problems-question-8an-automatic-cutter-machine","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-problems-question-8an-automatic-cutter-machine\/","title":{"rendered":"Hypothesis Testing Problems \u2013 Question 8(An automatic cutter machine\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 8 (One-sample t-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-problem-quesion-7-test-wether-cars-get-better-mileage\/\">\u2190 Question 7<\/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-9-wilcoxon-signed-rank-test\/\">Question 9 \u2192<\/a><\/nav>\n<div style=\"color: #555555; font-size: 18px; line-height: 30px; text-align: justify;\">\n<div style=\"font-family: 'segoe ui';\"> <span style=\"color: #cc0000;\"><span style=\"font-size: large;\"><b>Question&nbsp;<\/b><\/span><\/span> <br \/>An automatic cutter machine must cut steel strips of 1200 mm lenght. From a preliminary data, we checked that the lenghts of the pieces produced by the machine can be considered as normal random variables&nbsp; with a 3mm standard deviation. We want to make sure that the machine is set currectly. Therefore 16 pieces of the products are randomly selected and weight. The figures were in mm:<br \/>1193,1196,1198,1195,1198,1199,1204,1193,1203,1201,1196,1200,1191,1196,1198,1191<br \/>Examine wether there is any significant deviation from the required size<\/p>\n<p><span style=\"color: #38761d;\"><span style=\"font-size: large;\"><b>Solution Steps<\/b><\/span><\/span><br \/>As usual, try to understand the question so we can choose a test to use. From the question:<\/p>\n<ul>\n<li>the standard deviation of the sample is given<\/li>\n<li>the population is said to be normally distributed<\/li>\n<\/ul>\n<p>So we can safely use one-sample t-test<\/p>\n<p>Let&#8217;s follow the six easy steps of performing z-test.<br \/>Note: Some texts refer to this test as u-test <\/p>\n<p><b>Step 1:<\/b> State the null and the alternate hypothesis<\/p>\n<p><b>H<sub>0<\/sub>:<\/b> \u03bc<sub>0<\/sub> = \u03bc<sub>1<\/sub><br \/><b>H<sub>a<\/sub><\/b>: \u03bc<sub>0<\/sub> \u2260 \u03bc<sub>1<\/sub><\/p>\n<p><b>Step 2:<\/b> Calculate the mean of the sample<br \/>Mean = 1197<\/p>\n<p><b>Step 3: <\/b>Calculate the test statistic<br \/>This is gotten using the formula and the steps<\/p>\n<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/2.bp.blogspot.com\/-a_7LQm7zue8\/Wp6XWK5qCOI\/AAAAAAAABFU\/F9fChTNvUJsYnRzNtNbICnf5BnOy8N8IgCLcBGAs\/s1600\/z-test-for-cutter.jpg\" style=\"margin-left: 1em; margin-right: 1em;\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"476\" data-original-width=\"312\" height=\"320\" src=\"https:\/\/2.bp.blogspot.com\/-a_7LQm7zue8\/Wp6XWK5qCOI\/AAAAAAAABFU\/F9fChTNvUJsYnRzNtNbICnf5BnOy8N8IgCLcBGAs\/s320\/z-test-for-cutter.jpg\" width=\"209\" \/><\/a><\/div>\n<p><b>Step 4:<\/b> Look up value of z from the statistical table and compare with the calculated value<\/p>\n<p>From the table of z statistic we look up the critical value of z for 15 degrees of freedom and 0.05 significance<br \/><a href=\"https:\/\/kindsonthegenius.com\/blog\/statistical-tables\/\" target=\"_blank\" rel=\"noopener noreferrer\">Statistical table here<\/a><\/p>\n<p>This give us 0.0975 <\/p>\n<p><b>Step 5:<\/b> Draw a conclution<br \/>Since the calculated value of z is greater than the critical value, we reject the null hypothesis<\/p>\n<\/div>\n<\/div>\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> One-sample t-test<\/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 8 (One-sample t-test). Part of the 20 hypothesis testing solved examples series. \u2190 Question 7 \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":[544],"class_list":["post-152","post","type-post","status-publish","format-standard","hentry","category-hypothesis-testing","tag-hypothesis-testing"],"_links":{"self":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/152","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=152"}],"version-history":[{"count":3,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/152\/revisions"}],"predecessor-version":[{"id":2225,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/152\/revisions\/2225"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=152"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=152"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}