{"id":190601,"date":"2025-02-12T12:50:55","date_gmt":"2025-02-12T12:50:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=190601"},"modified":"2025-02-12T12:50:58","modified_gmt":"2025-02-12T12:50:58","slug":"you-also-can-find-the-t-statistic-on-statcrunch","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/12\/you-also-can-find-the-t-statistic-on-statcrunch\/","title":{"rendered":"You also can find the t-statistic on StatCrunch"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">You also can find the t-statistic on StatCrunch. If you are given summary statistics, go to<br>StatT Stats Two Sample > With Summary.<br>To test if two populations have different means, a random sample of 74 people from the first population had a mean of 17.3 standard deviation of 4.1. A random sample of 83 people from the second population had a mean of 19.2 and standard deviation of 3.7. Use these summary statistics to compute t and the p-value on StatCrunch. Round to four decimal places.<br>t<br>p-value-<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine whether two populations have different means, we can perform a two-sample t-test using the provided summary statistics. Here&#8217;s how to compute the t-statistic and p-value:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Given Data:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sample 1:<\/strong><\/li>\n\n\n\n<li>Sample size ((n_1)): 74<\/li>\n\n\n\n<li>Sample mean ((\\overline{x}_1)): 17.3<\/li>\n\n\n\n<li>Sample standard deviation ((s_1)): 4.1<\/li>\n\n\n\n<li><strong>Sample 2:<\/strong><\/li>\n\n\n\n<li>Sample size ((n_2)): 83<\/li>\n\n\n\n<li>Sample mean ((\\overline{x}_2)): 19.2<\/li>\n\n\n\n<li>Sample standard deviation ((s_2)): 3.7<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: Calculate the Pooled Standard Deviation<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The pooled standard deviation ((s_p)) is calculated using the formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ s_p = \\sqrt{\\frac{(n_1 &#8211; 1) \\cdot s_1^2 + (n_2 &#8211; 1) \\cdot s_2^2}{n_1 + n_2 &#8211; 2}} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituting the given values:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ s_p = \\sqrt{\\frac{(74 &#8211; 1) \\cdot 4.1^2 + (83 &#8211; 1) \\cdot 3.7^2}{74 + 83 &#8211; 2} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ s_p = \\sqrt{\\frac{73 \\cdot 16.81 + 82 \\cdot 13.69}{155}} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ s_p = \\sqrt{\\frac{1222.33 + 1125.48}{155}} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ s_p = \\sqrt{\\frac{2347.81}{155}} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ s_p \\approx \\sqrt{15.14} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ s_p \\approx 3.89 ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2: Calculate the Standard Error of the Difference Between Means<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The standard error ((SE)) of the difference between the two sample means is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ SE = s_p \\cdot \\sqrt{\\frac{1}{n_1} + \\frac{1}{n_2}} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituting the values:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ SE = 3.89 \\cdot \\sqrt{\\frac{1}{74} + \\frac{1}{83}} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ SE = 3.89 \\cdot \\sqrt{0.01351 + 0.01205} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ SE = 3.89 \\cdot \\sqrt{0.02556} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ SE \\approx 3.89 \\cdot 0.160 ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ SE \\approx 0.623 ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 3: Calculate the t-Statistic<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The t-statistic ((t)) is calculated as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ t = \\frac{\\overline{x}_1 &#8211; \\overline{x}_2}{SE} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituting the values:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ t = \\frac{17.3 &#8211; 19.2}{0.623} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ t = \\frac{-1.9}{0.623} ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ t \\approx -3.05 ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 4: Determine the Degrees of Freedom<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The degrees of freedom ((df)) for the t-test is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ df = n_1 + n_2 &#8211; 2 ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ df = 74 + 83 &#8211; 2 ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[ df = 155 ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 5: Find the p-Value<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using a t-distribution table or statistical software with (df = 155) and (t = -3.05), we find the p-value. For a two-tailed test, the p-value is approximately 0.0025.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Conclusion:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the p-value (0.0025) is less than the common significance level of 0.05, we reject the null hypothesis. This indicates that there is a statistically significant difference between the means of the two populations.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Using StatCrunch:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To perform this analysis in StatCrunch:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Navigate to <strong>Stat > T Stats > Two Sample > With Summary<\/strong>.<\/li>\n\n\n\n<li>Enter the sample sizes, means, and standard deviations for both samples.<\/li>\n\n\n\n<li>Select the appropriate hypothesis test (e.g., two-tailed).<\/li>\n\n\n\n<li>Click <strong>Compute<\/strong> to obtain the t-statistic and p-value.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">For a visual demonstration, you can refer to the following tutorial:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ue200video\ue202Two Sample t Test in StatCrunch\ue202turn0search1\ue201<\/p>\n","protected":false},"excerpt":{"rendered":"<p>You also can find the t-statistic on StatCrunch. If you are given summary statistics, go toStatT Stats Two Sample > With Summary.To test if two populations have different means, a random sample of 74 people from the first population had a mean of 17.3 standard deviation of 4.1. A random sample of 83 people from [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-190601","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190601","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=190601"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190601\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190601"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190601"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190601"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}