{"id":334,"date":"2016-04-21T22:43:40","date_gmt":"2016-04-21T22:43:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=chapter&#038;p=334"},"modified":"2017-07-12T18:10:37","modified_gmt":"2017-07-12T18:10:37","slug":"introduction-hypothesis-testing-with-two-samples-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/chapter\/introduction-hypothesis-testing-with-two-samples-2\/","title":{"raw":"Introduction: Hypothesis Testing with One Sample","rendered":"Introduction: Hypothesis Testing with One Sample"},"content":{"raw":"<div>\r\n<div class=\"media-header\">\r\n<div class=\"info\">\r\n<div class=\"downloads\">Page by: <span class=\"page-authors\">OpenStax<\/span><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div>\r\n<div class=\"media-body\">\r\n<div id=\"content\" data-is-baked=\"false\">\r\n<figure id=\"fs-idm165993648\" class=\"splash ui-has-child-figcaption\"><span id=\"fs-idm52702960\" data-type=\"media\" data-alt=\"This is a picture of a Dalmation dog covered in black spots. He is wearing a red color, appears to be in a nature setting, and there is a spout of water from a water fountain in the foreground.\"><img class=\"aligncenter\" src=\"https:\/\/cnx.org\/resources\/3a6073daae1d4d0cc130787dc9e5805034a8f7b2\/CNX_Stats_C09_CO.jpg\" alt=\"This is a picture of a Dalmation dog covered in black spots. He is wearing a red color, appears to be in a nature setting, and there is a spout of water from a water fountain in the foreground.\" width=\"380\" data-media-type=\"image\/jpeg\" \/><\/span><figcaption>You can use a hypothesis test to decide if a dog breeder\u2019s claim that every Dalmatian has 35 spots is statistically sound. (Credit: Robert Neff)<\/figcaption><\/figure>\r\n<div id=\"fs-idp21504400\" 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-667\">By the end of this chapter, the student should be able to:<\/p>\r\n\r\n<ul id=\"list67\">\r\n \t<li>Differentiate between Type I and Type II Errors<\/li>\r\n \t<li>Describe hypothesis testing in general and in practice<\/li>\r\n \t<li>Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.<\/li>\r\n \t<li>Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.<\/li>\r\n \t<li>Conduct and interpret hypothesis tests for a single population proportion.<\/li>\r\n<\/ul>\r\n<\/section><\/div>\r\nOne job of a statistician is to make statistical inferences about populations based on samples taken from the population. <span data-type=\"term\">Confidence intervals<\/span> are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.\r\n\r\n<\/div>\r\n<\/header><\/div>\r\n<p id=\"element-818\">A statistician will make a decision about these claims. This process is called \"<span data-type=\"term\">hypothesis testing<\/span>.\" A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analyses of the data, to reject the null hypothesis.<\/p>\r\n<p id=\"element-224\">In this chapter, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.<\/p>\r\n<p id=\"element-616\">Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:<\/p>\r\n\r\n<div id=\"list-1\" data-type=\"list\" data-list-type=\"enumerated\">\r\n<div data-type=\"item\">\r\n<div class=\"textbox examples\">\r\n<h3>Excercise<\/h3>\r\n<div id=\"list-1\" data-type=\"list\" data-list-type=\"enumerated\">\r\n<div data-type=\"item\">Set up two contradictory hypotheses.<\/div>\r\n<div data-type=\"item\">Collect sample data (in homework problems, the data or summary statistics will be given to you).<\/div>\r\n<div data-type=\"item\">Determine the correct distribution to perform the hypothesis test.<\/div>\r\n<div data-type=\"item\">Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.<\/div>\r\n<div data-type=\"item\">Make a decision and write a meaningful conclusion.<\/div>\r\n<\/div>\r\n<div id=\"id23787041\" class=\"note 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=\"\">NOTE<\/div>\r\n<\/header><section>\r\n<p id=\"eip-idm82174448\">To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. See <a href=\"https:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@18.55:c0449c55-aa47-4f1c-bd5f-0521652f0e82@5\" data-page=\"1\">Appendix E<\/a>.<\/p>\r\n\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div data-type=\"glossary\">\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"coninter\" class=\"definition\">\r\n \t<dt>Confidence Interval (CI)<\/dt>\r\n \t<dd id=\"id20495395\">an interval estimate for an unknown population parameter. This depends on:\r\n<ul id=\"confint1\">\r\n \t<li>The desired confidence level.<\/li>\r\n \t<li>Information that is known about the distribution (for example, known standard deviation).<\/li>\r\n \t<li>The sample and its size.<\/li>\r\n<\/ul>\r\n<\/dd>\r\n<\/dl>\r\n<dl id=\"hypotest\" class=\"definition\">\r\n \t<dt>Hypothesis Testing<\/dt>\r\n \t<dd id=\"id23787132\">Based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected, or is unreasonable and should be rejected.<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div>\n<div class=\"media-header\">\n<div class=\"info\">\n<div class=\"downloads\">Page by: <span class=\"page-authors\">OpenStax<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<div class=\"media-body\">\n<div id=\"content\" data-is-baked=\"false\">\n<figure id=\"fs-idm165993648\" class=\"splash ui-has-child-figcaption\"><span id=\"fs-idm52702960\" data-type=\"media\" data-alt=\"This is a picture of a Dalmation dog covered in black spots. He is wearing a red color, appears to be in a nature setting, and there is a spout of water from a water fountain in the foreground.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/cnx.org\/resources\/3a6073daae1d4d0cc130787dc9e5805034a8f7b2\/CNX_Stats_C09_CO.jpg\" alt=\"This is a picture of a Dalmation dog covered in black spots. He is wearing a red color, appears to be in a nature setting, and there is a spout of water from a water fountain in the foreground.\" width=\"380\" data-media-type=\"image\/jpeg\" \/><\/span><figcaption>You can use a hypothesis test to decide if a dog breeder\u2019s claim that every Dalmatian has 35 spots is statistically sound. (Credit: Robert Neff)<\/figcaption><\/figure>\n<div id=\"fs-idp21504400\" 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-667\">By the end of this chapter, the student should be able to:<\/p>\n<ul id=\"list67\">\n<li>Differentiate between Type I and Type II Errors<\/li>\n<li>Describe hypothesis testing in general and in practice<\/li>\n<li>Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.<\/li>\n<li>Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.<\/li>\n<li>Conduct and interpret hypothesis tests for a single population proportion.<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<p>One job of a statistician is to make statistical inferences about populations based on samples taken from the population. <span data-type=\"term\">Confidence intervals<\/span> are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.<\/p>\n<\/div>\n<\/header>\n<\/div>\n<p id=\"element-818\">A statistician will make a decision about these claims. This process is called &#8220;<span data-type=\"term\">hypothesis testing<\/span>.&#8221; A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analyses of the data, to reject the null hypothesis.<\/p>\n<p id=\"element-224\">In this chapter, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.<\/p>\n<p id=\"element-616\">Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:<\/p>\n<div id=\"list-1\" data-type=\"list\" data-list-type=\"enumerated\">\n<div data-type=\"item\">\n<div class=\"textbox examples\">\n<h3>Excercise<\/h3>\n<div id=\"list-1\" data-type=\"list\" data-list-type=\"enumerated\">\n<div data-type=\"item\">Set up two contradictory hypotheses.<\/div>\n<div data-type=\"item\">Collect sample data (in homework problems, the data or summary statistics will be given to you).<\/div>\n<div data-type=\"item\">Determine the correct distribution to perform the hypothesis test.<\/div>\n<div data-type=\"item\">Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.<\/div>\n<div data-type=\"item\">Make a decision and write a meaningful conclusion.<\/div>\n<\/div>\n<div id=\"id23787041\" class=\"note 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=\"\">NOTE<\/div>\n<\/header>\n<section>\n<p id=\"eip-idm82174448\">To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. See <a href=\"https:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@18.55:c0449c55-aa47-4f1c-bd5f-0521652f0e82@5\" data-page=\"1\">Appendix E<\/a>.<\/p>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"coninter\" class=\"definition\">\n<dt>Confidence Interval (CI)<\/dt>\n<dd id=\"id20495395\">an interval estimate for an unknown population parameter. This depends on:<\/p>\n<ul id=\"confint1\">\n<li>The desired confidence level.<\/li>\n<li>Information that is known about the distribution (for example, known standard deviation).<\/li>\n<li>The sample and its size.<\/li>\n<\/ul>\n<\/dd>\n<\/dl>\n<dl id=\"hypotest\" class=\"definition\">\n<dt>Hypothesis Testing<\/dt>\n<dd id=\"id23787132\">Based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected, or is unreasonable and should be rejected.<\/dd>\n<\/dl>\n<\/div>\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-334\">\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-334","chapter","type-chapter","status-publish","hentry"],"part":330,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/334","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/334\/revisions"}],"predecessor-version":[{"id":1463,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/334\/revisions\/1463"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/parts\/330"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/334\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/media?parent=334"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapter-type?post=334"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/contributor?post=334"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/license?post=334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}