{"id":416,"date":"2022-05-18T16:39:22","date_gmt":"2022-05-18T16:39:22","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/accintrostats\/chapter\/hypothesis-testing-for-two-means-and-two-proportions\/"},"modified":"2022-11-09T16:31:08","modified_gmt":"2022-11-09T16:31:08","slug":"hypothesis-testing-for-two-means-and-two-proportions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.ccconline.org\/accintrostats\/chapter\/hypothesis-testing-for-two-means-and-two-proportions\/","title":{"raw":"Activity 11.5: Hypothesis Testing for Two Means and Two Proportions","rendered":"Activity 11.5: Hypothesis Testing for Two Means and Two Proportions"},"content":{"raw":"&nbsp;\r\n<div id=\"fs-id1918441\" class=\"statistics lab\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\r\n<div data-type=\"title\">Hypothesis Testing for Two Means and Two Proportions<\/div>\r\n<p id=\"id5260693\">Class Time:<\/p>\r\n<p id=\"id6186867\">Names:<\/p>\r\n<p id=\"fs-idm110643216\"><span data-type=\"title\">Student Learning Outcomes<\/span><\/p>\r\n\r\n<ul id=\"id3866304\">\r\n \t<li>The student will select the appropriate distributions to use in each case.<\/li>\r\n \t<li>The student will conduct hypothesis tests and interpret the results.<\/li>\r\n<\/ul>\r\n<div id=\"id6083673\" data-type=\"list\">\r\n<div data-type=\"title\">Supplies:<\/div>\r\n<ul>\r\n \t<li>the business section from two consecutive days\u2019 newspapers<\/li>\r\n \t<li>three small packages of M&amp;Ms\u00ae<\/li>\r\n \t<li>five small packages of Reese's Pieces\u00ae<\/li>\r\n<\/ul>\r\n<\/div>\r\n<span data-type=\"title\">Increasing Stocks Survey<\/span><span data-type=\"newline\">\r\n<\/span>Look at yesterday\u2019s newspaper business section. Conduct a hypothesis test to determine if the proportion of New York Stock Exchange (NYSE) stocks that increased is greater than the proportion of NASDAQ stocks that increased. As randomly as possible, choose 40 NYSE stocks, and 32 NASDAQ stocks and complete the following statements.\r\n<ol id=\"list-86476434\" data-mark-suffix=\".\">\r\n \t<li><em data-effect=\"italics\">H<sub>0<\/sub>: _________<\/em><\/li>\r\n \t<li><em data-effect=\"italics\">H<sub>a<\/sub>: _________<\/em><\/li>\r\n \t<li>In words, define the random variable.<\/li>\r\n \t<li>The distribution to use for the test is _____________.<\/li>\r\n \t<li>Calculate the test statistic using your data.<\/li>\r\n \t<li>Draw a graph and label it appropriately. Shade the actual level of significance.\r\n<ol id=\"list-875872354\" type=\"a\">\r\n \t<li>Graph:\r\n<div id=\"id6690350\" class=\"bc-figure figure\"><span id=\"id6690354\" data-type=\"media\" data-alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\"><img src=\"https:\/\/pressbooks.ccconline.org\/acccomposition1\/wp-content\/uploads\/sites\/83\/2022\/05\/fig-ch10_11_02-1.png\" alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/div><\/li>\r\n \t<li>Calculate the <em data-effect=\"italics\">p<\/em>-value.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Do you reject or not reject the null hypothesis? Why?<\/li>\r\n \t<li>Write a clear conclusion using a complete sentence.<\/li>\r\n<\/ol>\r\n<span data-type=\"title\">Decreasing Stocks Survey<\/span> <span data-type=\"newline\">\r\n<\/span>Randomly pick eight stocks from the newspaper. Using two consecutive days\u2019 business sections, test whether the stocks went down, on average, for the second day.\r\n<ol data-mark-suffix=\".\">\r\n \t<li><em data-effect=\"italics\">H<sub>0<\/sub><\/em>: ________<\/li>\r\n \t<li><em data-effect=\"italics\">H<sub>a<\/sub>: ________<\/em><\/li>\r\n \t<li>In words, define the random variable.<\/li>\r\n \t<li>The distribution to use for the test is _____________.<\/li>\r\n \t<li>Calculate the test statistic using your data.<\/li>\r\n \t<li>Draw a graph and label it appropriately. Shade the actual level of significance.\r\n<ol id=\"list-8758723552564\" type=\"a\">\r\n \t<li>Graph:\r\n<div id=\"id8343352\" class=\"bc-figure figure\"><span id=\"id8343356\" data-type=\"media\" data-alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\"><img src=\"https:\/\/pressbooks.ccconline.org\/acccomposition1\/wp-content\/uploads\/sites\/83\/2022\/05\/fig-ch10_11_02-1.png\" alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/div><\/li>\r\n \t<li>Calculate the <em data-effect=\"italics\">p<\/em>-value:<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Do you reject or not reject the null hypothesis? Why?<\/li>\r\n \t<li>Write a clear conclusion using a complete sentence.<\/li>\r\n<\/ol>\r\n<p id=\"element-97568234\"><span data-type=\"title\">Candy Survey<\/span> Buy three small packages of M&amp;Ms and five small packages of Reese's Pieces (same net weight as the M&amp;Ms). Test whether or not the mean number of candy pieces per package is the same for the two brands.<\/p>\r\n\r\n<ol id=\"list343\" data-mark-suffix=\".\">\r\n \t<li><em data-effect=\"italics\">H<sub>0<\/sub><\/em>: ________<\/li>\r\n \t<li><em data-effect=\"italics\">H<sub>a<\/sub><\/em>: ________<\/li>\r\n \t<li>In words, define the random variable.<\/li>\r\n \t<li>What distribution should be used for this test?<\/li>\r\n \t<li>Calculate the test statistic using your data.<\/li>\r\n \t<li>Draw a graph and label it appropriately. Shade the actual level of significance.\r\n<ol id=\"list-896293765\" type=\"a\">\r\n \t<li>Graph:\r\n<div id=\"id8343564\" class=\"bc-figure figure\"><span id=\"id8343568\" data-type=\"media\" data-alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\"><img src=\"https:\/\/pressbooks.ccconline.org\/acccomposition1\/wp-content\/uploads\/sites\/83\/2022\/08\/fig-ch10_11_03-1.png\" alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/div><\/li>\r\n \t<li>Calculate the <em data-effect=\"italics\">p<\/em>-value.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Do you reject or not reject the null hypothesis? Why?<\/li>\r\n \t<li>Write a clear conclusion using a complete sentence.<\/li>\r\n<\/ol>\r\n<p id=\"element-858234\"><span data-type=\"title\">Shoe Survey<\/span> Test whether women have, on average, more pairs of shoes than men. Include all forms of sneakers, shoes, sandals, and boots. Use your class as the sample.<\/p>\r\n\r\n<ol id=\"list287\" data-mark-suffix=\".\">\r\n \t<li><em data-effect=\"italics\">H<sub>0<\/sub><\/em>: ________<\/li>\r\n \t<li><em data-effect=\"italics\">H<sub>a<\/sub><\/em>: ________<\/li>\r\n \t<li>In words, define the random variable.<\/li>\r\n \t<li>The distribution to use for the test is ________________.<\/li>\r\n \t<li>Calculate the test statistic using your data.<\/li>\r\n \t<li>Draw a graph and label it appropriately. Shade the actual level of significance.\r\n<ol id=\"list-8758723875552564\" type=\"a\">\r\n \t<li>Graph:\r\n<div id=\"id8357842\" class=\"bc-figure figure\"><span id=\"id8357847\" data-type=\"media\" data-alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\"><img src=\"https:\/\/pressbooks.ccconline.org\/acccomposition1\/wp-content\/uploads\/sites\/83\/2022\/08\/fig-ch10_11_04-1.png\" alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/div><\/li>\r\n \t<li>Calculate the <em data-effect=\"italics\">p<\/em>-value.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Do you reject or not reject the null hypothesis? Why?<\/li>\r\n \t<li>Write a clear conclusion using a complete sentence.<\/li>\r\n<\/ol>\r\n<\/div>","rendered":"<p>&nbsp;<\/p>\n<div id=\"fs-id1918441\" class=\"statistics lab\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<div data-type=\"title\">Hypothesis Testing for Two Means and Two Proportions<\/div>\n<p id=\"id5260693\">Class Time:<\/p>\n<p id=\"id6186867\">Names:<\/p>\n<p id=\"fs-idm110643216\"><span data-type=\"title\">Student Learning Outcomes<\/span><\/p>\n<ul id=\"id3866304\">\n<li>The student will select the appropriate distributions to use in each case.<\/li>\n<li>The student will conduct hypothesis tests and interpret the results.<\/li>\n<\/ul>\n<div id=\"id6083673\" data-type=\"list\">\n<div data-type=\"title\">Supplies:<\/div>\n<ul>\n<li>the business section from two consecutive days\u2019 newspapers<\/li>\n<li>three small packages of M&amp;Ms\u00ae<\/li>\n<li>five small packages of Reese&#8217;s Pieces\u00ae<\/li>\n<\/ul>\n<\/div>\n<p><span data-type=\"title\">Increasing Stocks Survey<\/span><span data-type=\"newline\"><br \/>\n<\/span>Look at yesterday\u2019s newspaper business section. Conduct a hypothesis test to determine if the proportion of New York Stock Exchange (NYSE) stocks that increased is greater than the proportion of NASDAQ stocks that increased. As randomly as possible, choose 40 NYSE stocks, and 32 NASDAQ stocks and complete the following statements.<\/p>\n<ol id=\"list-86476434\" data-mark-suffix=\".\">\n<li><em data-effect=\"italics\">H<sub>0<\/sub>: _________<\/em><\/li>\n<li><em data-effect=\"italics\">H<sub>a<\/sub>: _________<\/em><\/li>\n<li>In words, define the random variable.<\/li>\n<li>The distribution to use for the test is _____________.<\/li>\n<li>Calculate the test statistic using your data.<\/li>\n<li>Draw a graph and label it appropriately. Shade the actual level of significance.\n<ol id=\"list-875872354\" type=\"a\">\n<li>Graph:\n<div id=\"id6690350\" class=\"bc-figure figure\"><span id=\"id6690354\" data-type=\"media\" data-alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.ccconline.org\/acccomposition1\/wp-content\/uploads\/sites\/83\/2022\/05\/fig-ch10_11_02-1.png\" alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/div>\n<\/li>\n<li>Calculate the <em data-effect=\"italics\">p<\/em>-value.<\/li>\n<\/ol>\n<\/li>\n<li>Do you reject or not reject the null hypothesis? Why?<\/li>\n<li>Write a clear conclusion using a complete sentence.<\/li>\n<\/ol>\n<p><span data-type=\"title\">Decreasing Stocks Survey<\/span> <span data-type=\"newline\"><br \/>\n<\/span>Randomly pick eight stocks from the newspaper. Using two consecutive days\u2019 business sections, test whether the stocks went down, on average, for the second day.<\/p>\n<ol data-mark-suffix=\".\">\n<li><em data-effect=\"italics\">H<sub>0<\/sub><\/em>: ________<\/li>\n<li><em data-effect=\"italics\">H<sub>a<\/sub>: ________<\/em><\/li>\n<li>In words, define the random variable.<\/li>\n<li>The distribution to use for the test is _____________.<\/li>\n<li>Calculate the test statistic using your data.<\/li>\n<li>Draw a graph and label it appropriately. Shade the actual level of significance.\n<ol id=\"list-8758723552564\" type=\"a\">\n<li>Graph:\n<div id=\"id8343352\" class=\"bc-figure figure\"><span id=\"id8343356\" data-type=\"media\" data-alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.ccconline.org\/acccomposition1\/wp-content\/uploads\/sites\/83\/2022\/05\/fig-ch10_11_02-1.png\" alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/div>\n<\/li>\n<li>Calculate the <em data-effect=\"italics\">p<\/em>-value:<\/li>\n<\/ol>\n<\/li>\n<li>Do you reject or not reject the null hypothesis? Why?<\/li>\n<li>Write a clear conclusion using a complete sentence.<\/li>\n<\/ol>\n<p id=\"element-97568234\"><span data-type=\"title\">Candy Survey<\/span> Buy three small packages of M&amp;Ms and five small packages of Reese&#8217;s Pieces (same net weight as the M&amp;Ms). Test whether or not the mean number of candy pieces per package is the same for the two brands.<\/p>\n<ol id=\"list343\" data-mark-suffix=\".\">\n<li><em data-effect=\"italics\">H<sub>0<\/sub><\/em>: ________<\/li>\n<li><em data-effect=\"italics\">H<sub>a<\/sub><\/em>: ________<\/li>\n<li>In words, define the random variable.<\/li>\n<li>What distribution should be used for this test?<\/li>\n<li>Calculate the test statistic using your data.<\/li>\n<li>Draw a graph and label it appropriately. Shade the actual level of significance.\n<ol id=\"list-896293765\" type=\"a\">\n<li>Graph:\n<div id=\"id8343564\" class=\"bc-figure figure\"><span id=\"id8343568\" data-type=\"media\" data-alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.ccconline.org\/acccomposition1\/wp-content\/uploads\/sites\/83\/2022\/08\/fig-ch10_11_03-1.png\" alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/div>\n<\/li>\n<li>Calculate the <em data-effect=\"italics\">p<\/em>-value.<\/li>\n<\/ol>\n<\/li>\n<li>Do you reject or not reject the null hypothesis? Why?<\/li>\n<li>Write a clear conclusion using a complete sentence.<\/li>\n<\/ol>\n<p id=\"element-858234\"><span data-type=\"title\">Shoe Survey<\/span> Test whether women have, on average, more pairs of shoes than men. Include all forms of sneakers, shoes, sandals, and boots. Use your class as the sample.<\/p>\n<ol id=\"list287\" data-mark-suffix=\".\">\n<li><em data-effect=\"italics\">H<sub>0<\/sub><\/em>: ________<\/li>\n<li><em data-effect=\"italics\">H<sub>a<\/sub><\/em>: ________<\/li>\n<li>In words, define the random variable.<\/li>\n<li>The distribution to use for the test is ________________.<\/li>\n<li>Calculate the test statistic using your data.<\/li>\n<li>Draw a graph and label it appropriately. Shade the actual level of significance.\n<ol id=\"list-8758723875552564\" type=\"a\">\n<li>Graph:\n<div id=\"id8357842\" class=\"bc-figure figure\"><span id=\"id8357847\" data-type=\"media\" data-alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.ccconline.org\/acccomposition1\/wp-content\/uploads\/sites\/83\/2022\/08\/fig-ch10_11_04-1.png\" alt=\"This is a blank graph template. The vertical and horizontal axes are unlabeled.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/div>\n<\/li>\n<li>Calculate the <em data-effect=\"italics\">p<\/em>-value.<\/li>\n<\/ol>\n<\/li>\n<li>Do you reject or not reject the null hypothesis? Why?<\/li>\n<li>Write a clear conclusion using a complete sentence.<\/li>\n<\/ol>\n<\/div>\n","protected":false},"author":32,"menu_order":5,"template":"","meta":{"pb_show_title":"","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-416","chapter","type-chapter","status-publish","hentry"],"part":382,"_links":{"self":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/chapters\/416","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/users\/32"}],"version-history":[{"count":2,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/chapters\/416\/revisions"}],"predecessor-version":[{"id":696,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/chapters\/416\/revisions\/696"}],"part":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/parts\/382"}],"metadata":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/chapters\/416\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/media?parent=416"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/chapter-type?post=416"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/contributor?post=416"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/license?post=416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}