{"id":629,"date":"2024-06-19T09:14:46","date_gmt":"2024-06-19T06:14:46","guid":{"rendered":"https:\/\/sisu.ut.ee\/measurement\/self-test-10-5-b\/"},"modified":"2024-06-19T09:14:46","modified_gmt":"2024-06-19T06:14:46","slug":"self-test-10-5-b","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/measurement\/self-test-10-5-b\/","title":{"rendered":"Self-test 10.5 B"},"content":{"rendered":"<div id=\"watupro_quiz\" class=\"quiz-area single-page-quiz\">\n<p id=\"submittingExam29\" style=\"display:none;text-align:center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/img\/loading.gif\" width=\"16\" height=\"16\"><\/p>\n\n<div class=\"watupro-exam-description\" id=\"description-quiz-29\"><p>Here you can test your understanding of the single-lab validation approach and your ability to apply it in practice.<\/p>\n<\/div>\n\n<form action=\"\" method=\"post\" class=\"quiz-form\" id=\"quiz-29\" enctype=\"multipart\/form-data\">\n<div class=\"watu-question \" id=\"question-1\" style=\";\"><div id=\"questionWrap-1\" class=\"   watupro-question-id-109\">\n\t\t\t<div class=\"question-content\"><div>This exercise is based on exercises 10.2 and 10.3, it is their combination.<br>\r\n<br>\r\nA laboratory wants to estimate the measurement uncertainty of protein content determination in different foods. For this protein content in a control sample of smoked sausage was determined repeatedly during a time period of almost one year. Every day when this smoked sausage was analysed only one parallel measurement was made. The following results were obtained:<br>\r\n<br>\r\n\u00a0<br>\r\n<table style=\"width: 37.6249%; height: 375px;\" border=\"1px solid rgb(0, 0, 0)\" width=\"128\" cellpadding=\"4\"><tbody><tr><td style=\"border: 1px solid #000000; text-align: center;\" width=\"64\"><strong>Week<\/strong><\/td><td style=\"border: 1px solid #000000; text-align: center;\" width=\"64\"><strong>Result\u00a0(g\/100g)<\/strong><\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">3<\/td><td style=\"border: 1px solid #000000; text-align: center;\">18.1<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">5<\/td><td style=\"border: 1px solid #000000; text-align: center;\">20.5<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">11<\/td><td style=\"border: 1px solid #000000; text-align: center;\">18.3<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">14<\/td><td style=\"border: 1px solid #000000; text-align: center;\">19.1<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">15<\/td><td style=\"border: 1px solid #000000; text-align: center;\">19.3<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">27<\/td><td style=\"border: 1px solid #000000; text-align: center;\">20.2<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">34<\/td><td style=\"border: 1px solid #000000; text-align: center;\">19.7<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">41<\/td><td style=\"border: 1px solid #000000; text-align: center;\">19.5<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">42<\/td><td style=\"border: 1px solid #000000; text-align: center;\">18.6<\/td><\/tr><tr><td style=\"border: 1px solid #000000; text-align: center;\">48<\/td><td style=\"border: 1px solid #000000; text-align: center;\">20.1<\/td><\/tr><\/tbody><\/table>\u00a0<br>\r\n<br>\r\nIn addition the laboratory analysed two certified reference materials: Ham with protein content (19.6 \u00b1 0.6) g\/100g (<em>k<\/em>=2, norm) and cheese with protein content (26.3 \u00b1 0.7) g\/100g (<em>k<\/em>=2, norm). The laboratory has carried out four bias determinations with the following results (each found value is found as a mean from a number of parallel measurements):<br>\r\n<br>\r\n\u00a0<br>\r\n<table style=\"height: 120px; width: 19.3207%;\" border=\"1px solid rgb(0, 0, 0)\" width=\"19.3207%\" cellpadding=\"2\"><tbody><tr style=\"height: 24px;\"><td style=\"width: 136.812px; border: 1px solid #000000; height: 24px;\">Reference\u00a0(g\/100g)<\/td><td style=\"width: 153.615px; border: 1px solid #000000; height: 24px;\">Found\u00a0value\u00a0(g\/100g)<\/td><\/tr><tr style=\"height: 24px;\"><td style=\"width: 136.812px; border: 1px solid #000000; height: 24px;\">26.3<\/td><td style=\"width: 153.615px; border: 1px solid #000000; height: 24px;\">26.9<\/td><\/tr><tr style=\"height: 24px;\"><td style=\"width: 136.812px; border: 1px solid #000000; height: 24px;\">26.3<\/td><td style=\"width: 153.615px; border: 1px solid #000000; height: 24px;\">27.2<\/td><\/tr><tr style=\"height: 24px;\"><td style=\"width: 136.812px; border: 1px solid #000000; height: 24px;\">19.6<\/td><td style=\"width: 153.615px; border: 1px solid #000000; height: 24px;\">20.1<\/td><\/tr><tr style=\"height: 24px;\"><td style=\"width: 136.812px; border: 1px solid #000000; height: 24px;\">19.6<\/td><td style=\"width: 153.615px; border: 1px solid #000000; height: 24px;\">20.4<\/td><\/tr><\/tbody><\/table>\u00a0<br>\r\n<br>\r\nPlease calculate the combined standard uncertainty of the protein determination procedure (please give 1 or 2 decimals). Absolute uncertainties can be used in this case.<br>\r\n<br>\r\n\u00a0<br>\r\n<div class=\"accordion-block mb-3\"><div id=\"accordion-accordion-6683c25b1287520\" class=\"accordion \"><div class=\"accordion-item accordion-item--white\"><h3 id=\"accordion-6683c25b128752-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b1287520-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b1287520-collapse-2\">Clue 1 <\/button><\/h3><div id=\"accordion-6683c25b1287520-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b1287520-heading-1\"><div class=\"accordion-body\"><div>The reproducibility component is found as the standard deviation of the results obtained on different days.<\/div><\/div><\/div><\/div><\/div><\/div><div class=\"accordion-block mb-3\"><div id=\"accordion-accordion-6683c25b12875\" class=\"accordion \"><div class=\"accordion-item accordion-item--white\"><h3 id=\"accordion-6683c25b12875-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b12875-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b12875-collapse-1\">Clue 2<\/button><\/h3><div id=\"accordion-6683c25b12875-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b12875-heading-1\"><div class=\"accordion-body\"><div>The bias component is found as follows:<br>\r\n<br>\r\n<img loading=\"lazy\" decoding=\"async\" width=\"249\" height=\"37\" class=\"alignnone wp-image-288\" title=\"10-3-2-vihje1.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/10-3-2-vihje1.png\" alt=\"10-3-2-vihje1.png\">For finding the RMSbias and u(Cref) the bias values from the individual bias determinations (four altogether) and combined standard uncertainties of the reference materials used for the individual determinations (again, four altogether) have to be combined using the root mean square approach:<br>\r\n<br>\r\n<img loading=\"lazy\" decoding=\"async\" width=\"198\" height=\"143\" class=\"alignnone wp-image-289\" title=\"10-3-2-vihje1b.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/10-3-2-vihje1b.png\" alt=\"10-3-2-vihje1b.png\"><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"accordion-block mb-3\"><div id=\"accordion-accordion-6683c25b128752\" class=\"accordion \"><div class=\"accordion-item accordion-item--white\"><h3 id=\"accordion-6683c25b128752-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b128752-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b128752-collapse-2\">Clue 3<\/button><\/h3><div id=\"accordion-6683c25b128752-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b128752-heading-1\"><div class=\"accordion-body\"><div>The individual bias values are found as differences of the lab value and the reference value. The combined standard uncertainties of the reference values can be found by dividing the expanded uncertainties with the coverage factor.<\/div><\/div><\/div><\/div><\/div><\/div><div class=\"accordion-block mb-3\"><div id=\"accordion-accordion-6683c25b128753\" class=\"accordion \"><div class=\"accordion-item accordion-item--white\"><h3 id=\"accordion-6683c25b128753-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b128753-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b128753-collapse-1\">Clue 4<\/button><\/h3><div id=\"accordion-6683c25b128753-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b128753-heading-1\"><div class=\"accordion-body\"><div>The individual bias values are (all in g\/100g): 0.6, 0.9, 0.5, 0.8. The <em>RMS<\/em><sub>bias<\/sub> found from these data is 0.7176 g\/100g (decimal places are deliberately given in excess).<\/div><\/div><\/div><\/div><\/div><\/div><div class=\"accordion-block mb-3\"><div id=\"accordion-accordion-6683c25b128754\" class=\"accordion \"><div class=\"accordion-item accordion-item--white\"><h3 id=\"accordion-6683c25b128754-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b128754-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b128754-collapse-1\">Clue 5<\/button><\/h3><div id=\"accordion-6683c25b128754-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b128754-heading-1\"><div class=\"accordion-body\"><div>The individual <em>u<\/em>(<em>Cref<sub>i<\/sub><\/em>) values are (all in g\/100g): 0.35, 0.35, 0.3, 0.3. The <em>u<\/em>(<em>Cref<\/em>) found from these data is 0.3260 g\/100g (decimal places are deliberately given in excess).<\/div><\/div><\/div><\/div><\/div><\/div><div class=\"accordion-block mb-3\"><div id=\"accordion-accordion-6683c25b128755\" class=\"accordion \"><div class=\"accordion-item accordion-item--white\"><h3 id=\"accordion-6683c25b128755-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b128755-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b128755-collapse-1\">Clue 6<\/button><\/h3><div id=\"accordion-6683c25b128755-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b128755-heading-1\"><div class=\"accordion-body\"><div>The <em>u<\/em>(<em>bias<\/em>) found from these data is 0.7882 g\/100g (decimal places are deliberately given in excess). <em>u<\/em>(<em>bias<\/em>) is not yet the final uncertainty but rather an interim result for future calculations, so it should not be rounded to 1 or 2 significant digits.<\/div><\/div><\/div><\/div><\/div><\/div><\/div><input type=\"hidden\" name=\"question_id[]\" id=\"qID_1\" value=\"109\" class=\"watupro-question-id\"><input type=\"hidden\" id=\"answerType109\" class=\"answerTypeCnt1\" value=\"textarea\"><!-- end question-content--><\/div><div class=\"question-choices \" id=\"questionChoices109\"><p><input type=\"text\" name=\"answer-109[]\" id=\"textarea_q_109\" class=\"watupro-text\" value=\"\" size=\"60\"><\/p><!-- end question-choices--><\/div><!-- end questionWrap--><\/div><\/div><div style=\"display:none\" id=\"question-2\">\n\t<div class=\"question-content\">\n\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/img\/loading.gif\" width=\"16\" height=\"16\" alt=\"Loading...\" title=\"Loading...\">\u00a0Loading...\t<\/div>\n<\/div>\n\n<br>\n\t\n\t\t\t<div class=\"watupro_buttons flex \" id=\"watuPROButtons29\">\n\t\t  <div id=\"prev-question\" style=\"display:none;\"><input type=\"button\" value=\"&lt; Previous\" onclick=\"WatuPRO.nextQuestion(event, 'previous');\"><\/div>\t\t  \t\t  \t\t   \n\t\t   \t  \t\t<div><input type=\"button\" name=\"action\" class=\"watupro-submit-button\" onclick=\"WatuPRO.submitResult(event)\" id=\"action-button\" value=\"View Results\">\n\t\t<\/div>\n\t\t<\/div>\n\t\t\n\t<input type=\"hidden\" name=\"quiz_id\" value=\"29\" id=\"watuPROExamID\">\n\t<input type=\"hidden\" name=\"start_time\" id=\"startTime\" value=\"2026-04-19 23:29:09\">\n\t<input type=\"hidden\" name=\"start_timestamp\" id=\"startTimeStamp\" value=\"1776641349\">\n\t<input type=\"hidden\" name=\"question_ids\" value=\"\">\n\t<input type=\"hidden\" name=\"watupro_questions\" value=\"109:355,420\">\n\t<input type=\"hidden\" name=\"no_ajax\" value=\"0\">\t\t\t<\/form>\n\t<p>\u00a0<\/p>\n<\/div>\n\n<script type=\"text\/javascript\">\n\/\/jQuery(document).ready(function(){\ndocument.addEventListener(\"DOMContentLoaded\", function(event) { \t\nvar question_ids = \"109\";\nWatuPROSettings[29] = {};\nWatuPRO.qArr = question_ids.split(',');\nWatuPRO.exam_id = 29;\t    \nWatuPRO.post_id = 629;\nWatuPRO.store_progress = 0;\nWatuPRO.curCatPage = 1;\nWatuPRO.requiredIDs=\"0\".split(\",\");\nWatuPRO.hAppID = \"0.29941700 1776630549\";\nvar url = \"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/show_exam.php\";\nWatuPRO.examMode = 1;\nWatuPRO.siteURL=\"https:\/\/sisu.ut.ee\/measurement\/wp-admin\/admin-ajax.php\";\nWatuPRO.emailIsNotRequired = 0;\nWatuPRO.perDecade = 10;\nWatuPROIntel.init(29);\nWatuPRO.inCategoryPages=1;});    \t \n<\/script>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":280,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-629","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages\/629","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/users\/280"}],"replies":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/comments?post=629"}],"version-history":[{"count":0,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages\/629\/revisions"}],"wp:attachment":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/media?parent=629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}