{"id":20995,"date":"2025-06-14T21:24:23","date_gmt":"2025-06-14T21:24:23","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=20995"},"modified":"2025-06-14T21:24:24","modified_gmt":"2025-06-14T21:24:24","slug":"what-is-the-critical-value-of-0-02-assuming-two-tail-test","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-is-the-critical-value-of-0-02-assuming-two-tail-test\/","title":{"rendered":"what is the critical value of 0.02 assuming two tail test"},"content":{"rendered":"\n<p>what is the critical value of 0.02 assuming two tail test<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Correct Answer: \u00b12.33<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 Explanation (Two-Tailed Test with \u03b1 = 0.02)<\/h3>\n\n\n\n<p>In hypothesis testing, <strong>critical values<\/strong> determine the boundaries of the rejection region(s) for a specified level of significance (\u03b1). These values depend on:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Whether the test is <strong>one-tailed<\/strong> or <strong>two-tailed<\/strong><\/li>\n\n\n\n<li>The <strong>significance level (\u03b1)<\/strong><\/li>\n\n\n\n<li>The underlying <strong>distribution<\/strong> (often standard normal for z-tests)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd39 Step-by-Step Breakdown:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">1. <strong>Two-Tailed Test<\/strong><\/h4>\n\n\n\n<p>For a <strong>two-tailed test<\/strong>, the significance level is <strong>split between both tails<\/strong> of the standard normal distribution.<br>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total \u03b1 = 0.02<\/li>\n\n\n\n<li>Each tail = \u03b1\/2 = 0.01<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2. <strong>Use of the Z-distribution (Standard Normal)<\/strong><\/h4>\n\n\n\n<p>We&#8217;re assuming a <strong>z-test<\/strong>, which uses the <strong>standard normal distribution<\/strong> (mean = 0, SD = 1).<\/p>\n\n\n\n<p>We now find the z-scores that leave <strong>0.01 in the lower tail<\/strong> and <strong>0.01 in the upper tail<\/strong>, leaving <strong>0.98 in the middle<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">3. <strong>Using Z-tables or Calculator<\/strong><\/h4>\n\n\n\n<p>Look up the z-score for <strong>area = 0.99<\/strong> (since you want 1% in the upper tail).<\/p>\n\n\n\n<p>From standard z-tables or calculators:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>z \u2248 <strong>2.33<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Because it&#8217;s a <strong>two-tailed<\/strong> test, the <strong>critical values are both positive and negative<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u00b12.33<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83c\udfaf Interpretation:<\/h3>\n\n\n\n<p>If your test statistic (z) is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Less than <strong>\u22122.33<\/strong> or<\/li>\n\n\n\n<li>Greater than <strong>+2.33<\/strong><br>\u2192 then you <strong>reject the null hypothesis<\/strong> at the 0.02 level of significance.<\/li>\n<\/ul>\n\n\n\n<p>If the z falls <strong>between \u22122.33 and +2.33<\/strong>, then you <strong>fail to reject<\/strong> the null.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udccc Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significance level (\u03b1)<\/strong>: 0.02<\/li>\n\n\n\n<li><strong>Tail type<\/strong>: Two-tailed<\/li>\n\n\n\n<li><strong>Critical values<\/strong>: <strong>\u22122.33 and +2.33<\/strong><\/li>\n\n\n\n<li>These define the cutoff points for rejecting the null hypothesis.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>what is the critical value of 0.02 assuming two tail test The correct answer and explanation is: \u2705 Correct Answer: \u00b12.33 \ud83d\udcd8 Explanation (Two-Tailed Test with \u03b1 = 0.02) In hypothesis testing, critical values determine the boundaries of the rejection region(s) for a specified level of significance (\u03b1). These values depend on: \ud83d\udd39 Step-by-Step Breakdown: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-20995","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20995","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=20995"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20995\/revisions"}],"predecessor-version":[{"id":20996,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20995\/revisions\/20996"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=20995"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=20995"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=20995"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}