{"id":1213,"date":"2023-06-22T02:09:11","date_gmt":"2023-06-22T02:09:11","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-apply-it-1\/"},"modified":"2025-05-16T03:33:29","modified_gmt":"2025-05-16T03:33:29","slug":"null-and-alternative-hypotheses-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-apply-it-1\/","title":{"raw":"Null and Alternative Hypotheses: Apply It 1","rendered":"Null and Alternative Hypotheses: 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;Write a null and alternative hypothesis for a hypothesis test&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;}\">Write a null and alternative hypothesis for a hypothesis test.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Decide if a sample statistic provides enough evidence to reject the null hypothesis&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;}\">Decide if a sample statistic provides enough evidence to reject the null hypothesis.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Statistics is an important tool that helps us make inferences about a population when we are only able to consider a sample. Hypothesis testing can be used to explore whether there has been a change in a particular population parameter or whether a parameter is actually different than what had previously been assumed.<\/p>\r\n<h2>Testing the Waters<\/h2>\r\n<p><img class=\"size-medium wp-image-5523 alignright\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-300x300.jpg\" alt=\"An overhead archway sign reading 'FLINT VEHICLE CITY' against a cloudy sky, with the silhouette of a building in the background.\" width=\"300\" height=\"300\" \/><\/p>\r\n<p>In 2014, residents of Flint, Michigan began to suspect their water was contaminated with lead after the city switched its water source. The Michigan Department of Environmental Quality (DEQ) conducted an investigation and found Flint\u2019s water to be compliant with federal water safety regulations, which require that under [latex]10\\%[\/latex] of homes yield water samples that have lead levels of [latex]15[\/latex] parts per billion (ppb) or above. However, the residents of the city were not convinced, and they took their own sample of residences as part of the Flint Water Study (FWS).[footnote]Barry-Jester, A. M. (2016, January 26). <em>What went wrong in Flint.<\/em> FiveThirtyEight. <a href=\"https:\/\/fivethirtyeight.com\/features\/what-went-wrong-in-flint-water-crisis-michigan\/\">https:\/\/fivethirtyeight.com\/features\/what-went-wrong-in-flint-water-crisis-michigan\/<\/a>[\/footnote]<\/p>\r\n<div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1691[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1692[\/ohm2_question]<\/section>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a hypothesis test&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;}\">Write a null and alternative hypothesis for a hypothesis test.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Decide if a sample statistic provides enough evidence to reject the null hypothesis&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;}\">Decide if a sample statistic provides enough evidence to reject the null hypothesis.<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Statistics is an important tool that helps us make inferences about a population when we are only able to consider a sample. Hypothesis testing can be used to explore whether there has been a change in a particular population parameter or whether a parameter is actually different than what had previously been assumed.<\/p>\n<h2>Testing the Waters<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5523 alignright\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-300x300.jpg\" alt=\"An overhead archway sign reading 'FLINT VEHICLE CITY' against a cloudy sky, with the silhouette of a building in the background.\" width=\"300\" height=\"300\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-300x300.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-1024x1024.jpg 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-150x150.jpg 150w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-768x768.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-1536x1536.jpg 1536w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-2048x2048.jpg 2048w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-1200x1200.jpg 1200w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-65x65.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-225x225.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/09183327\/bruno-guerrero-uk5H5f4ZSPI-unsplash_batcheditor_fotor-350x350.jpg 350w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>In 2014, residents of Flint, Michigan began to suspect their water was contaminated with lead after the city switched its water source. The Michigan Department of Environmental Quality (DEQ) conducted an investigation and found Flint\u2019s water to be compliant with federal water safety regulations, which require that under [latex]10\\%[\/latex] of homes yield water samples that have lead levels of [latex]15[\/latex] parts per billion (ppb) or above. However, the residents of the city were not convinced, and they took their own sample of residences as part of the Flint Water Study (FWS).<a class=\"footnote\" title=\"Barry-Jester, A. M. (2016, January 26). What went wrong in Flint. FiveThirtyEight. https:\/\/fivethirtyeight.com\/features\/what-went-wrong-in-flint-water-crisis-michigan\/\" id=\"return-footnote-1213-1\" href=\"#footnote-1213-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1691\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1691&theme=lumen&iframe_resize_id=ohm1691&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1692\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1692&theme=lumen&iframe_resize_id=ohm1692&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1213-1\">Barry-Jester, A. M. (2016, January 26). <em>What went wrong in Flint.<\/em> FiveThirtyEight. <a href=\"https:\/\/fivethirtyeight.com\/features\/what-went-wrong-in-flint-water-crisis-michigan\/\">https:\/\/fivethirtyeight.com\/features\/what-went-wrong-in-flint-water-crisis-michigan\/<\/a> <a href=\"#return-footnote-1213-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":12,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1205,"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\/1213"}],"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":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1213\/revisions"}],"predecessor-version":[{"id":6753,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1213\/revisions\/6753"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1205"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1213\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1213"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1213"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1213"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}