{"id":1330,"date":"2023-06-22T02:17:38","date_gmt":"2023-06-22T02:17:38","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-two-population-means-independent-samples-learn-it-2\/"},"modified":"2025-05-16T22:29:22","modified_gmt":"2025-05-16T22:29:22","slug":"comparing-two-population-means-independent-samples-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-two-population-means-independent-samples-learn-it-2\/","title":{"raw":"Comparing Two Population Means (Independent Samples): Learn It 2","rendered":"Comparing Two Population Means (Independent Samples): 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 two-sample t-test for independent population 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 two-sample [latex]t[\/latex]-test for independent population means from hypotheses to conclusions<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Difference of the Means<\/h2>\r\n<p>One way to compare the means of two groups is by looking at the difference of the means.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6758[\/ohm2_question]<\/section>\r\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">When we are interested in estimating a difference in population means using data from independent samples, we will use a two-sample [latex]t[\/latex] confidence interval or a two-sample [latex]t[\/latex]-test.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>conditions for two-sample [latex]t[\/latex]-test<\/h3>\r\n<ol>\r\n\t<li>The samples are independent.<\/li>\r\n\t<li>Each sample is a random sample from the corresponding population of interest, or it is reasonable to regard the sample as random. It is reasonable to regard the sample as a random sample if it was selected in a way that should result in a sample that is representative of the population. <strong>If the data are from an experiment, we just need to check that there was random assignment to experimental groups\u2014this substitutes for the random sample condition and also results in independent samples.<\/strong><\/li>\r\n\t<li>For each population, the distribution of the variable that was measured is approximately normal, or the sample size for the sample from that population is large. Usually, <strong>a sample of size [latex]30[\/latex] or more is considered to be \u201clarge.\u201d<\/strong> If a sample size is less than [latex]30[\/latex], you should look at a plot of the data from that sample (a dotplot, a boxplot, or, if the sample size isn\u2019t really small, a histogram) to make sure that the distribution looks approximately symmetric and that there are no outliers.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]5485[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a two-sample t-test for independent population 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 two-sample [latex]t[\/latex]-test for independent population means from hypotheses to conclusions<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Difference of the Means<\/h2>\n<p>One way to compare the means of two groups is by looking at the difference of the means.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6758\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6758&theme=lumen&iframe_resize_id=ohm6758&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">When we are interested in estimating a difference in population means using data from independent samples, we will use a two-sample [latex]t[\/latex] confidence interval or a two-sample [latex]t[\/latex]-test.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>conditions for two-sample [latex]t[\/latex]-test<\/h3>\n<ol>\n<li>The samples are independent.<\/li>\n<li>Each sample is a random sample from the corresponding population of interest, or it is reasonable to regard the sample as random. It is reasonable to regard the sample as a random sample if it was selected in a way that should result in a sample that is representative of the population. <strong>If the data are from an experiment, we just need to check that there was random assignment to experimental groups\u2014this substitutes for the random sample condition and also results in independent samples.<\/strong><\/li>\n<li>For each population, the distribution of the variable that was measured is approximately normal, or the sample size for the sample from that population is large. Usually, <strong>a sample of size [latex]30[\/latex] or more is considered to be \u201clarge.\u201d<\/strong> If a sample size is less than [latex]30[\/latex], you should look at a plot of the data from that sample (a dotplot, a boxplot, or, if the sample size isn\u2019t really small, a histogram) to make sure that the distribution looks approximately symmetric and that there are no outliers.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm5485\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=5485&theme=lumen&iframe_resize_id=ohm5485&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":21,"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\/1330"}],"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":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1330\/revisions"}],"predecessor-version":[{"id":6815,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1330\/revisions\/6815"}],"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\/1330\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1330"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1330"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1330"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}