{"id":199123,"date":"2025-03-10T18:48:33","date_gmt":"2025-03-10T18:48:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199123"},"modified":"2025-03-10T18:48:35","modified_gmt":"2025-03-10T18:48:35","slug":"a-recent-study-focused-on-the-number-of-times-people-18-to-25-years-old-and-25-to-35-years-old-send-a-twitter-message-in-a-day","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/10\/a-recent-study-focused-on-the-number-of-times-people-18-to-25-years-old-and-25-to-35-years-old-send-a-twitter-message-in-a-day\/","title":{"rendered":"A recent study focused on the number of times people 18 to 25 years old and 25 to 35 years old send a Twitter message in a day"},"content":{"rendered":"\n<p>A recent study focused on the number of times people 18 to 25 years old and 25 to 35 years old send a Twitter message in a day. The information is summarized here:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Age: 18 to 25<\/li>\n\n\n\n<li>Sample Size: 39<\/li>\n\n\n\n<li>Sample Mean: 37<\/li>\n\n\n\n<li>Population Standard Deviation: 5<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Age: 25 to 35<\/li>\n\n\n\n<li>Sample Size: 44<\/li>\n\n\n\n<li>Sample Mean: 42<\/li>\n\n\n\n<li>Population Standard Deviation: 10<\/li>\n<\/ul>\n\n\n\n<p>At the 0.01 significance level, we ask if there is a difference in the mean number of times people 18 to 25 years old and 25 to 35 years old send a Twitter message in a day. Assume that people 25 to 35 years old are Population 1 and people 18 to 25 years old are Population 2.<\/p>\n\n\n\n<p>What is the value of the test statistic for this hypothesis test? choose the write answer<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a. 3.195<\/li>\n\n\n\n<li>b. 3.199<\/li>\n\n\n\n<li>c. 2.929<\/li>\n\n\n\n<li>d. 3.103<\/li>\n<\/ul>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is:<\/p>\n\n\n\n<p><strong>c. 2.929<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This hypothesis test is used to determine whether there is a significant difference in the mean number of Twitter messages sent per day between the two age groups (18-25 and 25-35). Since the population standard deviations are known, we use a <strong>Z-test for two independent samples<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 1: Define the hypotheses<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Null Hypothesis (H0H_0)<\/strong>: There is no difference in the mean number of Twitter messages sent per day between the two age groups. H0:\u03bc1=\u03bc2H_0: \\mu_1 = \\mu_2<\/li>\n\n\n\n<li><strong>Alternative Hypothesis (HaH_a)<\/strong>: There is a difference in the mean number of Twitter messages sent per day. Ha:\u03bc1\u2260\u03bc2H_a: \\mu_1 \\neq \\mu_2<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 2: Compute the Test Statistic<\/strong><\/h4>\n\n\n\n<p>The test statistic for a <strong>two-sample Z-test<\/strong> is given by: Z=X1\u02c9\u2212X2\u02c9\u03c312n1+\u03c322n2Z = \\frac{\\bar{X_1} &#8211; \\bar{X_2}}{\\sqrt{\\frac{\\sigma_1^2}{n_1} + \\frac{\\sigma_2^2}{n_2}}}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>X1\u02c9=42\\bar{X_1} = 42 (sample mean for age 25-35)<\/li>\n\n\n\n<li>X2\u02c9=37\\bar{X_2} = 37 (sample mean for age 18-25)<\/li>\n\n\n\n<li>\u03c31=10\\sigma_1 = 10 (population standard deviation for age 25-35)<\/li>\n\n\n\n<li>\u03c32=5\\sigma_2 = 5 (population standard deviation for age 18-25)<\/li>\n\n\n\n<li>n1=44n_1 = 44 (sample size for age 25-35)<\/li>\n\n\n\n<li>n2=39n_2 = 39 (sample size for age 18-25)<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 3: Compute the Standard Error<\/strong><\/h4>\n\n\n\n<p>SE=10244+5239SE = \\sqrt{\\frac{10^2}{44} + \\frac{5^2}{39}} SE=10044+2539SE = \\sqrt{\\frac{100}{44} + \\frac{25}{39}} SE\u22482.2727+0.6410=2.9137\u22481.707SE \\approx \\sqrt{2.2727 + 0.6410} = \\sqrt{2.9137} \\approx 1.707<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 4: Compute the Z-score<\/strong><\/h4>\n\n\n\n<p>Z=42\u2212371.707=51.707\u22482.929Z = \\frac{42 &#8211; 37}{1.707} = \\frac{5}{1.707} \\approx 2.929<\/p>\n\n\n\n<p>Thus, the test statistic value is <strong>2.929<\/strong>, making the correct answer <strong>(c)<\/strong>.<\/p>\n\n\n\n<p>Now, let&#8217;s generate an image representing the hypothesis test.<\/p>\n\n\n\n<p>The image above illustrates the two-tailed Z-test for this hypothesis test. The <strong>red-shaded areas<\/strong> represent the rejection regions at a <strong>0.01 significance level<\/strong>, while the <strong>green dashed line<\/strong> marks the computed test statistic (<strong>Z = 2.929<\/strong>). Since the test statistic does not exceed the critical value for rejection (approximately <strong>\u00b12.576<\/strong> for a 0.01 significance level), the result suggests that we may need to further analyze whether we reject the null hypothesis.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-826-1024x689.png\" alt=\"\" class=\"wp-image-199124\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A recent study focused on the number of times people 18 to 25 years old and 25 to 35 years old send a Twitter message in a day. The information is summarized here: At the 0.01 significance level, we ask if there is a difference in the mean number of times people 18 to 25 [&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-199123","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199123","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=199123"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199123\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}