{"id":161,"date":"2018-03-03T12:56:00","date_gmt":"2018-03-03T11:56:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/03\/hypothesis-testing-problem-question-1in-a-population-the-average-iq\/"},"modified":"2026-07-13T00:26:02","modified_gmt":"2026-07-12T22:26:02","slug":"hypothesis-testing-problem-question-1in-a-population-the-average-iq","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-problem-question-1in-a-population-the-average-iq\/","title":{"rendered":"Hypothesis Testing Problem \u2013 Question 1(In a population, the average IQ\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 1 (One-sample z-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-solved-examplesquestions-and-solutions\/\">All 20 questions<\/a> \u00b7 <a href=\"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-problem-question-2-a-professor-wants-to-know-if\/\">Question 2 \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=\"font-size: large;\"><span style=\"color: #cc0000;\"><b>Question<\/b><\/span><\/span><br \/>In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists want to test a new medication to see if it has either a positive or negative effect on intelligence, or not effect at all. A sample of 30 participants who have taken the medication&nbsp; has a mean of 140. Did the medication affect intelligence?<\/p>\n<p><b><span style=\"color: #274e13;\"><span style=\"font-size: large;\">Solution Steps<\/span><\/span><\/b><br \/>Follow these simple steps in solving this question. Leave a question at the left of this page if you hava any.<\/p>\n<p><b>Step 1: Set up the null and alternate hypothesis<\/b><\/p>\n<p><b>H<sub>0<\/sub>:<\/b> medication affects intelligence<br \/><b>H<sub>a<\/sub><\/b>: medication does not affect intellignece<\/p>\n<p>(not that the alternate hypothesis is always the opposite of the null hypothesis)<\/p>\n<p><b>Step 2: Determine the type of test to use<\/b><br \/>Since the sample size&nbsp; is 30, we use the z-test. See why we use the z-test when sample size is 30 and above in <a href=\"https:\/\/kindsonthegenius.com\/blog\/parametric-tests-in-statistics-when-to-use-which\/\">Parametric Tests in Statistics, When to use which<\/a><\/p>\n<p><b>Step 3: Calculate the tested statistic z using the formula<\/b><\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/1.bp.blogspot.com\/-sJd-Y6HBfvc\/WpqW-56Ct7I\/AAAAAAAAA98\/InRsuHjLd0MDe_02MnF6j8jIIFQyji7cgCLcBGAs\/s1600\/z-test%2Bformularu.JPG.jpg\" style=\"margin-left: 1em; margin-right: 1em;\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"443\" data-original-width=\"689\" height=\"256\" src=\"https:\/\/1.bp.blogspot.com\/-sJd-Y6HBfvc\/WpqW-56Ct7I\/AAAAAAAAA98\/InRsuHjLd0MDe_02MnF6j8jIIFQyji7cgCLcBGAs\/s400\/z-test%2Bformularu.JPG.jpg\" width=\"400\" \/><\/a><\/div>\n<div style=\"clear: both; text-align: center;\"><\/div>\n<div style=\"clear: both; text-align: center;\"><\/div>\n<p>This formular can also be written like this:<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/1.bp.blogspot.com\/-Nk8ZH_JuDfA\/WpqWrzjZtKI\/AAAAAAAAA94\/pLXCLibgjV83ZnPIQZLsvwxwKROR5D_RwCLcBGAs\/s1600\/z-test%2Bformular2.jpg\" style=\"margin-left: 1em; margin-right: 1em;\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"95\" data-original-width=\"320\" height=\"58\" src=\"https:\/\/1.bp.blogspot.com\/-Nk8ZH_JuDfA\/WpqWrzjZtKI\/AAAAAAAAA94\/pLXCLibgjV83ZnPIQZLsvwxwKROR5D_RwCLcBGAs\/s200\/z-test%2Bformular2.jpg\" width=\"200\" \/><\/a><\/div>\n<p>Using the data given in the equation we would have the following:<br \/>\u03bc<sub>0<\/sub> = 100<br \/><span><span>\u03c3 = 15<\/span><\/span><br \/><span><span>n = 30<\/span><\/span><br \/><span><span>x\u0304<sub>n<\/sub> = 140&nbsp;<\/span><\/span><\/p>\n<p><span><span>Plugging the values into the formular we have:<\/span><\/span><\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/1.bp.blogspot.com\/-ojZHNm2OML0\/WpqXtn1a1II\/AAAAAAAAA-M\/KSuDOKjHKJQwQiell-NP0EAn0ZABDeMigCLcBGAs\/s1600\/z-test-for-question-1.jpg\" style=\"margin-left: 1em; margin-right: 1em;\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"101\" data-original-width=\"550\" height=\"58\" src=\"https:\/\/1.bp.blogspot.com\/-ojZHNm2OML0\/WpqXtn1a1II\/AAAAAAAAA-M\/KSuDOKjHKJQwQiell-NP0EAn0ZABDeMigCLcBGAs\/s320\/z-test-for-question-1.jpg\" width=\"320\" \/><\/a><\/div>\n<p><b>Step 4:&nbsp; Look up the values of z ( called the critical value) from statistical tables.&nbsp;<\/b><br \/>You can access statistical table from here. <a href=\"https:\/\/www.google.com.ng\/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=1&amp;cad=rja&amp;uact=8&amp;ved=0ahUKEwiq-f3RltDZAhXQzqQKHRo8AA4QFggoMAA&amp;url=https%3A%2F%2Fhome.ubalt.edu%2Fntsbarsh%2FBusiness-stat%2FStatistialTables.pdf&amp;usg=AOvVaw0q50SBMrvT0j_hBuErJJ3q\" target=\"_blank\" rel=\"noopener noreferrer\">Statistical Table<\/a><br \/>From the table: we get a value of 1.96<\/p>\n<p><b>Step 5: Draw a conclusion<\/b><br \/>In this case the tested statistic value of z calculated is more than the critical value obtained from statistical tables.<\/p>\n<p>14.606 &gt; 1.96 <\/p>\n<p>&nbsp;Therefore we reject the null hypothesis.<br \/>This means, from the question, that the medication administered does not affect intelligence. <\/p>\n<p>You can get video lessons from my YouTube Channel below. Also subscribe for regular updates.<br \/><a href=\"https:\/\/www.youtube.com\/channel\/UCvHgEAcw6VpcOA3864pSr5A\" target=\"_blank\" rel=\"noopener noreferrer\">Kindson The Genuis Lessons<\/a><\/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 z-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 1 (One-sample z-test). Part of the 20 hypothesis testing solved examples series. All 20 questions \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-161","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\/161","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=161"}],"version-history":[{"count":3,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/161\/revisions"}],"predecessor-version":[{"id":2218,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/161\/revisions\/2218"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=161"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=161"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}