{"id":414,"date":"2016-04-21T22:43:39","date_gmt":"2016-04-21T22:43:39","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=chapter&#038;p=414"},"modified":"2017-07-12T22:06:04","modified_gmt":"2017-07-12T22:06:04","slug":"introduction-the-chi-square-distribution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/chapter\/introduction-the-chi-square-distribution\/","title":{"raw":"Introduction: The Chi-Square Distribution","rendered":"Introduction: The Chi-Square Distribution"},"content":{"raw":"<div><\/div>\r\n<div>\r\n<div class=\"media-body\">\r\n<figure id=\"fs-idm45331472\" class=\"splash ui-has-child-figcaption\"><span id=\"CNX_Stats_C11_CO.jpg\" data-type=\"media\" data-alt=\"This is a photo of a pile of grocery store receipts. The items and prices are blurred.\"><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214747\/CNX_Stats_C11_CO.jpg\" alt=\"This is a photo of a pile of grocery store receipts. The items and prices are blurred.\" width=\"500\" data-media-type=\"image\/jpg\" \/><\/span><figcaption>The chi-square distribution can be used to find relationships between two things, like grocery prices at different stores. (credit: Pete\/flickr)<\/figcaption><\/figure>\r\n<div id=\"fs-idm151065040\" class=\"note chapter-objectives ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><header>\r\n<div class=\"title\" data-type=\"title\" data-label-parent=\"\">\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<section>\r\n<p id=\"element-335\">By the end of this chapter, the student should be able to:<\/p>\r\n\r\n<ul id=\"element-377\" data-bullet-style=\"bullet\">\r\n \t<li>Interpret the chi-square probability distribution as the sample size changes.<\/li>\r\n \t<li>Conduct and interpret chi-square goodness-of-fit hypothesis tests.<\/li>\r\n \t<li>Conduct and interpret chi-square test of independence hypothesis tests.<\/li>\r\n \t<li>Conduct and interpret chi-square homogeneity hypothesis tests.<\/li>\r\n \t<li>Conduct and interpret chi-square single variance hypothesis tests.<\/li>\r\n<\/ul>\r\n<\/section><\/div>\r\nHave you ever wondered if lottery numbers were evenly distributed or if some numbers occurred with a greater frequency? How about if the types of movies people preferred were different across different age groups? What about if a coffee machine was dispensing approximately the same amount of coffee each time? You could answer these questions by conducting a hypothesis test.\r\n\r\n<\/div>\r\n<\/header><\/div>\r\n<p id=\"element-8\">You will now study a new distribution, one that is used to determine the answers to such questions. This distribution is called the chi-square distribution.<\/p>\r\nIn this chapter, you will learn the three major applications of the chi-square distribution:\r\n<div id=\"list-9872341\" data-type=\"list\" data-list-type=\"enumerated\">\r\n<div data-type=\"item\">the goodness-of-fit test, which determines if data fit a particular distribution, such as in the lottery example<\/div>\r\n<div data-type=\"item\">the test of independence, which determines if events are independent, such as in the movie example<\/div>\r\n<div data-type=\"item\">the test of a single variance, which tests variability, such as in the coffee example<\/div>\r\n<\/div>\r\n<div id=\"id17641525\" class=\"note finger ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><header>\r\n<div data-type=\"title\" data-label-parent=\"\"><\/div>\r\n<div class=\"title\" data-type=\"title\" data-label-parent=\"\">NOTE<\/div>\r\n<div class=\"title\" data-type=\"title\" data-label-parent=\"\">Though the chi-square distribution depends on calculators or computers for most of the calculations, there is a table available. TI-83+ and TI-84 calculator instructions are included in the text.<\/div>\r\n<\/header><\/div>\r\n<div id=\"fs-idm94608208\" class=\"note statistics collab ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><header>\r\n<div class=\"title\" data-type=\"title\" data-label-parent=\"\">\r\n<div class=\"textbox examples\">\r\n<h3>Excercise<\/h3>\r\n<section>Look in the sports section of a newspaper or on the Internet for some sports data (baseball averages, basketball scores, golf tournament scores, football odds, swimming times, and the like). Plot a histogram and a boxplot using your data. See if you can determine a probability distribution that your data fits. Have a discussion with the class about your choice.\r\n\r\n<\/section><\/div>\r\n<\/div>\r\n<\/header><\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div><\/div>\n<div>\n<div class=\"media-body\">\n<figure id=\"fs-idm45331472\" class=\"splash ui-has-child-figcaption\"><span id=\"CNX_Stats_C11_CO.jpg\" data-type=\"media\" data-alt=\"This is a photo of a pile of grocery store receipts. The items and prices are blurred.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214747\/CNX_Stats_C11_CO.jpg\" alt=\"This is a photo of a pile of grocery store receipts. The items and prices are blurred.\" width=\"500\" data-media-type=\"image\/jpg\" \/><\/span><figcaption>The chi-square distribution can be used to find relationships between two things, like grocery prices at different stores. (credit: Pete\/flickr)<\/figcaption><\/figure>\n<div id=\"fs-idm151065040\" class=\"note chapter-objectives ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<header>\n<div class=\"title\" data-type=\"title\" data-label-parent=\"\">\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<section>\n<p id=\"element-335\">By the end of this chapter, the student should be able to:<\/p>\n<ul id=\"element-377\" data-bullet-style=\"bullet\">\n<li>Interpret the chi-square probability distribution as the sample size changes.<\/li>\n<li>Conduct and interpret chi-square goodness-of-fit hypothesis tests.<\/li>\n<li>Conduct and interpret chi-square test of independence hypothesis tests.<\/li>\n<li>Conduct and interpret chi-square homogeneity hypothesis tests.<\/li>\n<li>Conduct and interpret chi-square single variance hypothesis tests.<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<p>Have you ever wondered if lottery numbers were evenly distributed or if some numbers occurred with a greater frequency? How about if the types of movies people preferred were different across different age groups? What about if a coffee machine was dispensing approximately the same amount of coffee each time? You could answer these questions by conducting a hypothesis test.<\/p>\n<\/div>\n<\/header>\n<\/div>\n<p id=\"element-8\">You will now study a new distribution, one that is used to determine the answers to such questions. This distribution is called the chi-square distribution.<\/p>\n<p>In this chapter, you will learn the three major applications of the chi-square distribution:<\/p>\n<div id=\"list-9872341\" data-type=\"list\" data-list-type=\"enumerated\">\n<div data-type=\"item\">the goodness-of-fit test, which determines if data fit a particular distribution, such as in the lottery example<\/div>\n<div data-type=\"item\">the test of independence, which determines if events are independent, such as in the movie example<\/div>\n<div data-type=\"item\">the test of a single variance, which tests variability, such as in the coffee example<\/div>\n<\/div>\n<div id=\"id17641525\" class=\"note finger ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<header>\n<div data-type=\"title\" data-label-parent=\"\"><\/div>\n<div class=\"title\" data-type=\"title\" data-label-parent=\"\">NOTE<\/div>\n<div class=\"title\" data-type=\"title\" data-label-parent=\"\">Though the chi-square distribution depends on calculators or computers for most of the calculations, there is a table available. TI-83+ and TI-84 calculator instructions are included in the text.<\/div>\n<\/header>\n<\/div>\n<div id=\"fs-idm94608208\" class=\"note statistics collab ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<header>\n<div class=\"title\" data-type=\"title\" data-label-parent=\"\">\n<div class=\"textbox examples\">\n<h3>Excercise<\/h3>\n<section>Look in the sports section of a newspaper or on the Internet for some sports data (baseball averages, basketball scores, golf tournament scores, football odds, swimming times, and the like). Plot a histogram and a boxplot using your data. See if you can determine a probability distribution that your data fits. Have a discussion with the class about your choice.<\/p>\n<\/section>\n<\/div>\n<\/div>\n<\/header>\n<\/div>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-414\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Statistics . <strong>Authored by<\/strong>: Barbara Illowski, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\">http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Introductory Statistics \",\"author\":\"Barbara Illowski, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-414","chapter","type-chapter","status-publish","hentry"],"part":411,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/pressbooks\/v2\/chapters\/414","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/pressbooks\/v2\/chapters\/414\/revisions"}],"predecessor-version":[{"id":1474,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/pressbooks\/v2\/chapters\/414\/revisions\/1474"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/pressbooks\/v2\/parts\/411"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/pressbooks\/v2\/chapters\/414\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/wp\/v2\/media?parent=414"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/pressbooks\/v2\/chapter-type?post=414"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/wp\/v2\/contributor?post=414"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolk-introstats1\/wp-json\/wp\/v2\/license?post=414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}