{"id":1321,"date":"2023-06-22T02:17:31","date_gmt":"2023-06-22T02:17:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-means-learn-it-1\/"},"modified":"2024-01-22T22:37:58","modified_gmt":"2024-01-22T22:37:58","slug":"one-sample-hypothesis-test-for-means-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-means-learn-it-1\/","title":{"raw":"One-Sample Hypothesis Test for Means: Apply It 1","rendered":"One-Sample Hypothesis Test for Means: Apply It 1"},"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<section class=\"textbox recall\">\r\n<ul>\r\n\t<li>Notation for\u00a0<strong>population<\/strong> mean: [latex]\\mu[\/latex] (pronounce as \"mu\")<\/li>\r\n\t<li>Notation for\u00a0<strong>sample<\/strong> mean: [latex]\\bar{x}[\/latex] (pronounce as \"x-bar\")<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]993[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]996[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox recall\"><strong>Conditions for a One-Sample [latex]t[\/latex]-Test<\/strong>\r\n<ol>\r\n\t<li>The sample is a <strong>random sample<\/strong> from the population of interest or it is reasonable to regard the sample as if it is 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.<\/li>\r\n\t<li>For each population, the distribution of the variable that was measured is <strong>approximately normal, or the sample size for the sample from that population is large<\/strong>. Usually, a sample of size [latex]30[\/latex] or more is considered to be \u201clarge.\u201d 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>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]997[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]998[\/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 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<section class=\"textbox recall\">\n<ul>\n<li>Notation for\u00a0<strong>population<\/strong> mean: [latex]\\mu[\/latex] (pronounce as &#8220;mu&#8221;)<\/li>\n<li>Notation for\u00a0<strong>sample<\/strong> mean: [latex]\\bar{x}[\/latex] (pronounce as &#8220;x-bar&#8221;)<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm993\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=993&theme=lumen&iframe_resize_id=ohm993&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm996\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=996&theme=lumen&iframe_resize_id=ohm996&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox recall\"><strong>Conditions for a One-Sample [latex]t[\/latex]-Test<\/strong><\/p>\n<ol>\n<li>The sample is a <strong>random sample<\/strong> from the population of interest or it is reasonable to regard the sample as if it is 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.<\/li>\n<li>For each population, the distribution of the variable that was measured is <strong>approximately normal, or the sample size for the sample from that population is large<\/strong>. Usually, a sample of size [latex]30[\/latex] or more is considered to be \u201clarge.\u201d 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>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm997\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=997&theme=lumen&iframe_resize_id=ohm997&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm998\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=998&theme=lumen&iframe_resize_id=ohm998&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":17,"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":"apply_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\/1321"}],"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\/1321\/revisions"}],"predecessor-version":[{"id":5228,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1321\/revisions\/5228"}],"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\/1321\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1321"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1321"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1321"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}