{"id":1324,"date":"2023-06-22T02:17:33","date_gmt":"2023-06-22T02:17:33","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-means-apply-it-2\/"},"modified":"2025-05-16T22:23:11","modified_gmt":"2025-05-16T22:23:11","slug":"one-sample-hypothesis-test-for-means-apply-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-means-apply-it-2\/","title":{"raw":"One-Sample Hypothesis Test for Means: Learn It 2","rendered":"One-Sample Hypothesis Test for Means: Learn It 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a one-sample t-test for means from hypotheses to conclusions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Complete a one-sample [latex]t[\/latex]-test for means from hypotheses to conclusions.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Test Statistic ([latex]t[\/latex])<\/h2>\r\n<section>Let's revisit the \"<strong>plastics<\/strong>\" data set used previously in this class.\u00a0<\/section>\r\n<section><\/section>\r\n<section>Recall that this data set is a sample of plastic products collected by community volunteers in countries around the world during a brand audit to see what types of plastics are found in waste and which companies the plastics found came from.[reveal-answer q=\"11303\"]The Coca-Cola Company Dataset for 2020[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"11303\"]\r\n\r\n<table style=\"border-collapse: collapse; width: 192px; height: 1965px;\" border=\"0\" width=\"116\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl67\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">grand_total<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">44<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">122<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">95<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">78<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">119<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">6<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">204<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">29<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">136<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">134<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">132<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">20<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">5<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">147<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">14<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">7<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">258<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">2<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">93<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">219<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">13<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">20<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">1<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">3268<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">21<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">1<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">11<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">9<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">320<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">232<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">165<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">4068<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">9<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">614<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">6<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">27<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">40<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">9<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">2<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">647<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">28<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">256<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">775<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">423<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">12<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">126<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">497<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">39<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">247<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13.0pt;\">\r\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center;\" height=\"17\">85<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>[\/hidden-answer]<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/ \" width=\"100%\" height=\"1075\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]11104[\/ohm2_question]<\/section>\r\n<\/section>\r\n<section class=\"textbox recall\">Although calculating the [latex]t[\/latex]-statistic is just a matter of inputting the correct value into the formula and using a calculator, our statistical tool can calculate the value for you. Furthermore, it will calculate the P-value for us, which we can use to make a conclusion to answer the research question.\r\n\r\n<p>However, if you would like, you can calculate the test statistic using the formula below:<strong style=\"font-size: 0.9em; word-spacing: normal;\"><br \/>\r\n[latex]t[\/latex]-statistic:<\/strong><span style=\"background-color: initial; font-size: 0.9em; word-spacing: normal;\"> [latex]t=\\dfrac{\\stackrel{\u00af}{x}-\u03bc}{\\frac{s}{\\sqrt{n}}}[\/latex]<br \/>\r\n<\/span><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">The distribution of [latex]t[\/latex]-scores depends on the degrees of freedom, that is, [latex]df = n \u2013 1[\/latex].<\/span><\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1077[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]861[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]859[\/ohm2_question]<\/section>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a one-sample t-test for means from hypotheses to conclusions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Complete a one-sample [latex]t[\/latex]-test for means from hypotheses to conclusions.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Test Statistic ([latex]t[\/latex])<\/h2>\n<section>Let&#8217;s revisit the &#8220;<strong>plastics<\/strong>&#8221; data set used previously in this class.\u00a0<\/section>\n<section><\/section>\n<section>Recall that this data set is a sample of plastic products collected by community volunteers in countries around the world during a brand audit to see what types of plastics are found in waste and which companies the plastics found came from.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q11303\">The Coca-Cola Company Dataset for 2020<\/button><\/p>\n<div id=\"q11303\" class=\"hidden-answer\" style=\"display: none\">\n<table style=\"border-collapse: collapse; width: 192px; height: 1965px; width: 116px; border-spacing: 0px;\" cellpadding=\"0\">\n<tbody>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl67\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">grand_total<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">44<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">122<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">95<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">78<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">119<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">6<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">204<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">29<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">136<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">134<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">132<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">20<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">5<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">147<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">14<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">7<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">258<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">2<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">93<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">219<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">13<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">20<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">1<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">3268<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">21<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">1<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">11<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">9<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">320<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">232<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">165<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">4068<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">9<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">614<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">6<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">27<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">40<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">9<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">2<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">647<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">28<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">256<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">775<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">423<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">12<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">126<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">497<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">39<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">247<\/td>\n<\/tr>\n<tr style=\"height: 13.0pt;\">\n<td class=\"xl65\" style=\"height: 13pt; width: 248.333px; text-align: center; height: 17px;\">85<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/\" width=\"100%\" height=\"1075\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm11104\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=11104&theme=lumen&iframe_resize_id=ohm11104&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n<section class=\"textbox recall\">Although calculating the [latex]t[\/latex]-statistic is just a matter of inputting the correct value into the formula and using a calculator, our statistical tool can calculate the value for you. Furthermore, it will calculate the P-value for us, which we can use to make a conclusion to answer the research question.<\/p>\n<p>However, if you would like, you can calculate the test statistic using the formula below:<strong style=\"font-size: 0.9em; word-spacing: normal;\"><br \/>\n[latex]t[\/latex]-statistic:<\/strong><span style=\"background-color: initial; font-size: 0.9em; word-spacing: normal;\"> [latex]t=\\dfrac{\\stackrel{\u00af}{x}-\u03bc}{\\frac{s}{\\sqrt{n}}}[\/latex]<br \/>\n<\/span><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">The distribution of [latex]t[\/latex]-scores depends on the degrees of freedom, that is, [latex]df = n \u2013 1[\/latex].<\/span><\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1077\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1077&theme=lumen&iframe_resize_id=ohm1077&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm861\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=861&theme=lumen&iframe_resize_id=ohm861&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm859\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=859&theme=lumen&iframe_resize_id=ohm859&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n","protected":false},"author":8,"menu_order":15,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1309,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1324"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1324\/revisions"}],"predecessor-version":[{"id":6810,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1324\/revisions\/6810"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1309"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1324\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1324"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1324"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1324"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}