{"id":230704,"date":"2025-06-09T20:35:01","date_gmt":"2025-06-09T20:35:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230704"},"modified":"2025-06-09T20:35:05","modified_gmt":"2025-06-09T20:35:05","slug":"a-data-set-includes-110-body-temperatures-of-healthy-adult-humans-with-a-mean-of-98","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/a-data-set-includes-110-body-temperatures-of-healthy-adult-humans-with-a-mean-of-98\/","title":{"rendered":"A data set includes 110 body temperatures of healthy adult humans, with a mean of 98"},"content":{"rendered":"\n

A data set includes 110 body temperatures of healthy adult humans, with a mean of 98.1\u00c2\u00b0F and a standard deviation of 0.64\u00c2\u00b0F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6\u00c2\u00b0F as the mean body temperature? What is the confidence interval estimate of the population mean \u00ce\u00bc? What should replace the question marks? Round to three decimal places. ?\u00c2\u00b0F < \u00ce\u00bc < ?\u00c2\u00b0F What does this suggest about the use of 98.6\u00c2\u00b0F as the mean body temperature? Which letter is correct? A. This suggests that the mean body temperature could very possibly be 98.6\u00c2\u00b0F. B. This suggests that the mean body temperature could be higher than 98.6\u00c2\u00b0F. C. This suggests that the mean body temperature could be lower than 98.6\u00c2\u00b0F.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Given:<\/strong><\/h3>\n\n\n\n
    \n
  • Sample size, n = 110<\/strong><\/li>\n\n\n\n
  • Sample mean, x\u0304 = 98.1\u00b0F<\/strong><\/li>\n\n\n\n
  • Sample standard deviation, s = 0.64\u00b0F<\/strong><\/li>\n\n\n\n
  • Confidence level = 99%<\/strong><\/li>\n<\/ul>\n\n\n\n

    Step 1: Use the t-distribution<\/strong><\/h3>\n\n\n\n

    Since the population standard deviation is unknown and the sample size is large (>30), we can use the t-distribution<\/strong>.<\/p>\n\n\n\n

    Degrees of freedom:
    df = n – 1 = 109<\/strong><\/p>\n\n\n\n

    For a 99% confidence level and 109 degrees of freedom, the t-critical value (t*) \u2248 2.626<\/strong> (from a t-table or calculator).<\/p>\n\n\n\n

    Step 2: Calculate the standard error (SE)<\/strong><\/h3>\n\n\n\n

    SE=sn=0.64110\u22480.6410.4881\u22480.061SE = \\frac{s}{\\sqrt{n}} = \\frac{0.64}{\\sqrt{110}} \u2248 \\frac{0.64}{10.4881} \u2248 0.061SE=n\u200bs\u200b=110\u200b0.64\u200b\u224810.48810.64\u200b\u22480.061<\/p>\n\n\n\n

    Step 3: Construct the confidence interval<\/strong><\/h3>\n\n\n\n

    CI=x\u02c9\u00b1t\u2217\u22c5SE=98.1\u00b12.626\u22c50.061\u224898.1\u00b10.160CI = x\u0304 \\pm t^* \\cdot SE = 98.1 \\pm 2.626 \\cdot 0.061 \u2248 98.1 \\pm 0.160CI=x\u02c9\u00b1t\u2217\u22c5SE=98.1\u00b12.626\u22c50.061\u224898.1\u00b10.160CI\u2248(97.940,98.260)CI \u2248 (97.940, 98.260)CI\u2248(97.940,98.260)<\/p>\n\n\n\n

    Final Answer:<\/strong><\/h3>\n\n\n\n

    97.940\u00b0F < \u03bc < 98.260\u00b0F<\/strong><\/p>\n\n\n\n

    Interpretation and Analysis<\/strong><\/h3>\n\n\n\n

    The calculated 99% confidence interval for the population mean body temperature is approximately (97.940\u00b0F, 98.260\u00b0F)<\/strong>. This interval means we are 99% confident that the true average body temperature of all healthy adults falls within this range.<\/p>\n\n\n\n

    Historically, 98.6\u00b0F<\/strong> has been cited as the standard average human body temperature. However, this value does not<\/strong> fall within the computed confidence interval. Because the entire interval lies below 98.6\u00b0F<\/strong>, this suggests that the widely accepted average of 98.6\u00b0F may be an overestimate of the true mean.<\/p>\n\n\n\n

    The data set, derived from a sample of 110 healthy adults, provides strong evidence that the actual mean body temperature is lower than 98.6\u00b0F<\/strong>. Over time, multiple studies have challenged the 98.6\u00b0F standard, and this result further supports the notion that the average body temperature in modern populations is closer to 98.1\u00b0F or even slightly less.<\/p>\n\n\n\n

    Therefore, based on this confidence interval and statistical reasoning, we can infer that the mean body temperature for healthy adults is likely less than<\/strong> 98.6\u00b0F, and the historical standard may need to be updated in clinical practice.<\/p>\n\n\n\n

    Correct Choice:<\/strong><\/h3>\n\n\n\n

    C. This suggests that the mean body temperature could be lower than 98.6\u00b0F.<\/strong><\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    A data set includes 110 body temperatures of healthy adult humans, with a mean of 98.1\u00c2\u00b0F and a standard deviation of 0.64\u00c2\u00b0F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6\u00c2\u00b0F as the mean body temperature? What is the […]<\/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-230704","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230704","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=230704"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230704\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230704"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230704"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230704"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}