{"id":33807,"date":"2024-04-15T09:21:58","date_gmt":"2024-04-15T09:21:58","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=33807"},"modified":"2024-04-15T09:21:58","modified_gmt":"2024-04-15T09:21:58","slug":"the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/","title":{"rendered":"The difference of two means in case of small samples is tested by the formula:"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;$$t = \\frac{{\\overline {{x_1}} &#8211; \\overline {{x_2}} }}{S}$$&#8221; option2=&#8221;$$t = \\frac{{\\overline {{x_1}} &#8211; \\overline {{x_2}} }}{S}\\sqrt {\\frac{{{n_1} + {n_2}}}{{{n_1} &#8211; {n_2}}}} $$&#8221; option3=&#8221;$$t = \\frac{{\\overline {{x_1}} &#8211; \\overline {{x_2}} }}{S}\\sqrt {\\frac{{{n_1} &#8211; {n_2}}}{{{n_1} + {n_2}}}} $$&#8221; option4=&#8221;None of these&#8221; correct=&#8221;option2&#8243;]<!--more--><\/p>\n<p>The correct answer is: <strong>B. $t = \\frac{{\\overline {{x_1}} &#8211; \\overline {{x_2}} }}{S}\\sqrt {\\frac{{{n_1} + {n_2}}}{{{n_1} &#8211; {n_2}}}} $<\/strong><\/p>\n<p>The formula for the t-test for the difference of two means is:<\/p>\n<p>$$t = \\frac{{\\overline {{x_1}} &#8211; \\overline {{x_2}} }}{S}\\sqrt {\\frac{{{n_1} + {n_2}}}{{{n_1} &#8211; {n_2}}}} $$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$\\overline{{x_1}}$ is the mean of the first sample<\/li>\n<li>$\\overline{{x_2}}$ is the mean of the second sample<\/li>\n<li>$S$ is the pooled standard deviation<\/li>\n<li>$n_1$ is the number of observations in the first sample<\/li>\n<li>$n_2$ is the number of observations in the second sample<\/li>\n<\/ul>\n<p>The t-test is a statistical test that is used to compare the means of two groups. It is a parametric test, which means that it assumes that the data are normally distributed. The t-test can be used to test for a difference in means between two groups, or to test for a difference in means between two groups after adjusting for covariates.<\/p>\n<p>The t-test is a powerful test, but it is important to note that it is sensitive to the assumption of normality. If the data are not normally distributed, the t-test may not be accurate.<\/p>\n<p>The t-test is a versatile test that can be used in a variety of settings. It is a common test that is used in many fields, including statistics, psychology, and medicine.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;$$t = \\frac{{\\overline {{x_1}} &#8211; \\overline {{x_2}} }}{S}$$&#8221; option2=&#8221;$$t = \\frac{{\\overline {{x_1}} &#8211; \\overline {{x_2}} }}{S}\\sqrt {\\frac{{{n_1} + {n_2}}}{{{n_1} &#8211; {n_2}}}} $$&#8221; option3=&#8221;$$t = \\frac{{\\overline {{x_1}} &#8211; \\overline {{x_2}} }}{S}\\sqrt {\\frac{{{n_1} &#8211; {n_2}}}{{{n_1} + {n_2}}}} $$&#8221; option4=&#8221;None of these&#8221; correct=&#8221;option2&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[701],"tags":[],"class_list":["post-33807","post","type-post","status-publish","format-standard","hentry","category-business-statistics-and-research-methods","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The difference of two means in case of small samples is tested by the formula:<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The difference of two means in case of small samples is tested by the formula:\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;$$t = frac{{overline {{x_1}} &#8211; overline {{x_2}} }}{S}$$&#8221; option2=&#8221;$$t = frac{{overline {{x_1}} &#8211; overline {{x_2}} }}{S}sqrt {frac{{{n_1} + {n_2}}}{{{n_1} &#8211; {n_2}}}} $$&#8221; option3=&#8221;$$t = frac{{overline {{x_1}} &#8211; overline {{x_2}} }}{S}sqrt {frac{{{n_1} &#8211; {n_2}}}{{{n_1} + {n_2}}}} $$&#8221; option4=&#8221;None of these&#8221; correct=&#8221;option2&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T09:21:58+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The difference of two means in case of small samples is tested by the formula:","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/","og_locale":"en_US","og_type":"article","og_title":"The difference of two means in case of small samples is tested by the formula:","og_description":"[amp_mcq option1=&#8221;$$t = frac{{overline {{x_1}} &#8211; overline {{x_2}} }}{S}$$&#8221; option2=&#8221;$$t = frac{{overline {{x_1}} &#8211; overline {{x_2}} }}{S}sqrt {frac{{{n_1} + {n_2}}}{{{n_1} &#8211; {n_2}}}} $$&#8221; option3=&#8221;$$t = frac{{overline {{x_1}} &#8211; overline {{x_2}} }}{S}sqrt {frac{{{n_1} &#8211; {n_2}}}{{{n_1} + {n_2}}}} $$&#8221; option4=&#8221;None of these&#8221; correct=&#8221;option2&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T09:21:58+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/","name":"The difference of two means in case of small samples is tested by the formula:","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T09:21:58+00:00","dateModified":"2024-04-15T09:21:58+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-difference-of-two-means-in-case-of-small-samples-is-tested-by-the-formula\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Commerce","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/commerce\/"},{"@type":"ListItem","position":4,"name":"Business statistics and research methods","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/commerce\/business-statistics-and-research-methods\/"},{"@type":"ListItem","position":5,"name":"The difference of two means in case of small samples is tested by the formula:"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/33807","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=33807"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/33807\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=33807"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=33807"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=33807"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}