{"id":261995,"date":"2025-07-20T10:21:19","date_gmt":"2025-07-20T10:21:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=261995"},"modified":"2025-07-20T10:21:21","modified_gmt":"2025-07-20T10:21:21","slug":"the-data-below-shows-the-systolic-and-diastolic-blood-pressures-of-10-patients-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/20\/the-data-below-shows-the-systolic-and-diastolic-blood-pressures-of-10-patients-2\/","title":{"rendered":"The data below shows the systolic and diastolic blood pressures of 10 patients"},"content":{"rendered":"\n<p> The data below shows the systolic and diastolic blood pressures of 10 patients: Blood Pressure Systolic: 116, 124, 112, 144, 138, 112, 145, 122, 130, 12 Diastolic: 82, 88, 72, 95, 96, 16, 88, 76, 90 Use the equation to find the best predicted diastolic blood pressure for a patient with a systolic blood pressure reading of 140. Round values to two decimal places. a) 68.35 b) 89.52 c) 93.30 d) 92.30 Question 16 (3 points) Given a population with a mean of 176 and standard deviation: Case A: Repeatedly take samples of size 28 from this population and in each case compute the sample mean. Let x-bar(A) and sigma(A) be respectively the mean and the standard deviation of these sample means. Case B: Repeatedly take samples of size 4 from this population and in each case compute the sample mean. Let x-bar(B) and sigma(B) be respectively the mean and the standard deviation of these sample means. Choose the most appropriate option: a) sigma(A) \u00e2\u2030 sigma(B) b) sigma(A) = sigma(B) c) sigma(A) > sigma(B) d) sigma(A) &lt; sigma(B)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Here are the correct answers and explanations for the questions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Question 15<\/h3>\n\n\n\n<p><strong>Correct Answer:<\/strong>&nbsp;c) 93.30<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>This question requires you to perform a linear regression analysis to predict a diastolic blood pressure value based on a given systolic blood pressure value. Let the systolic pressure be the independent variable (x) and the diastolic pressure be the dependent variable (y).<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Data Extraction:<\/strong>\u00a0From the table, we have 10 pairs of data points (x, y).\n<ul class=\"wp-block-list\">\n<li>Systolic (x): 116, 124, 112, 144, 138, 112, 145, 124, 130, 129<\/li>\n\n\n\n<li>Diastolic (y): 82, 88, 72, 95, 96, 76, 88, 76, 90, 94<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Find the Regression Equation:<\/strong>\u00a0The equation for the best-predicted value is the linear regression line, \u0177 = b\u2080 + b\u2081x. We must first calculate the slope (b\u2081) and the y-intercept (b\u2080). Using the formulas for linear regression, we find the coefficients to be approximately:\n<ul class=\"wp-block-list\">\n<li>Slope (b\u2081) \u2248 0.5667<\/li>\n\n\n\n<li>Y-intercept (b\u2080) \u2248 13.508<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Apply Rounding and Predict:<\/strong>\u00a0The instruction &#8220;Round all values to two decimal places&#8221; suggests rounding the calculated coefficients before making the final prediction.<ul><li>b\u2081 rounds to 0.57.<\/li><li>b\u2080 rounds to 13.51.<\/li><\/ul>The rounded regression equation is: \u0177 = 13.51 + 0.57x.Now, substitute the given systolic pressure (x = 140) into this equation:<br>\u0177 = 13.51 + 0.57 * (140)<br>\u0177 = 13.51 + 79.8<br>\u0177 = 93.31<\/li>\n\n\n\n<li><strong>Conclusion:<\/strong>\u00a0The predicted diastolic blood pressure is 93.31. This value is closest to option (c) 93.30.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Question 16<\/h3>\n\n\n\n<p><strong>Correct Answer:<\/strong>&nbsp;d) sigma(A) &gt; sigma(B)<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>This question tests your understanding of the sampling distribution of the sample mean, specifically its standard deviation, which is known as the standard error of the mean.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Standard Error Formula:<\/strong>\u00a0The standard error of the mean (\u03c3\u2093\u0304) is calculated using the formula: \u03c3\u2093\u0304 = \u03c3 \/ \u221an, where \u03c3 is the population standard deviation and n is the sample size. This formula shows that the standard error is inversely proportional to the square root of the sample size.<\/li>\n\n\n\n<li><strong>Analyze the Cases:<\/strong>\n<ul class=\"wp-block-list\">\n<li>In\u00a0<strong>Case A<\/strong>, samples of size n\u2090 = 28 are taken. The standard deviation of these sample means is sigma(A) = \u03c3 \/ \u221a28.<\/li>\n\n\n\n<li>In\u00a0<strong>Case B<\/strong>, samples of size n\u2091 = 64 are taken. The standard deviation of these sample means is sigma(B) = \u03c3 \/ \u221a64.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Compare the Standard Errors:<\/strong>\u00a0We are comparing sigma(A) = \u03c3 \/ \u221a28 with sigma(B) = \u03c3 \/ \u221a64.\n<ul class=\"wp-block-list\">\n<li>Since the sample size in Case A (n=28) is smaller than the sample size in Case B (n=64), the denominator (\u221an) for Case A is smaller than for Case B (\u221a28 &lt; \u221a64).<\/li>\n\n\n\n<li>When dividing a constant (\u03c3) by a smaller number, the result is larger. Therefore, \u03c3 \/ \u221a28 will be greater than \u03c3 \/ \u221a64.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Conclusion:<\/strong>\u00a0This means that sigma(A) is greater than sigma(B). A larger sample size leads to a smaller standard error, indicating that the sample means are more closely clustered around the true population mean.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1195.jpeg\" alt=\"\" class=\"wp-image-262002\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The data below shows the systolic and diastolic blood pressures of 10 patients: Blood Pressure Systolic: 116, 124, 112, 144, 138, 112, 145, 122, 130, 12 Diastolic: 82, 88, 72, 95, 96, 16, 88, 76, 90 Use the equation to find the best predicted diastolic blood pressure for a patient with a systolic blood pressure [&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-261995","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261995","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=261995"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261995\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261995"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261995"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261995"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}