{"id":1075,"date":"2021-06-08T21:39:56","date_gmt":"2021-06-09T01:39:56","guid":{"rendered":"https:\/\/openbooks.macewan.ca\/rcommander\/?post_type=part&#038;p=1075"},"modified":"2023-12-28T21:35:08","modified_gmt":"2023-12-29T02:35:08","slug":"chapter-10-inferences-for-population-proportions","status":"publish","type":"part","link":"https:\/\/openbooks.macewan.ca\/introstats\/part\/chapter-10-inferences-for-population-proportions\/","title":{"raw":"Chapter 10: Inferences for Population Proportions","rendered":"Chapter 10: Inferences for Population Proportions"},"content":{"raw":"<h2><strong>Overview<\/strong><\/h2>\r\nChapters 8 and 9 introduced inferences for population means. This chapter focuses on inferences for another population parameter: <strong>the population proportion <em>p<\/em><\/strong>, defined as the proportion (or percentage) of a population with a specified attribute. For example, the proportion of times that athletes wearing blue uniforms win a judo match, the proportion of customers who respond to an advertisement, and the proportion of women who have arthritis.\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nAs a result of completing this chapter, you will be able to do the following:\r\n<ul>\r\n \t<li>Explain why the sample proportion [latex]\\hat{p} = \\frac{x}{n}[\/latex] is a special type of sample mean [latex]\\bar{x} = \\frac{\\sum x_i}{n}[\/latex].<\/li>\r\n \t<li>Describe the sampling distribution of the sample proportion [latex]\\hat{p}[\/latex].<\/li>\r\n \t<li>Conduct a one-proportion <i>z-test<\/i>.<\/li>\r\n \t<li>Obtain a [latex](1 - \\alpha) \\times 100%[\/latex] confidence interval for the population proportion [latex]p[\/latex].<\/li>\r\n \t<li>Describe the sampling distribution of the difference between two sample proportions [latex](\\hat{p}_1 - \\hat{p}_2)[\/latex].<\/li>\r\n \t<li>Conduct a two-proportion <i>z-test<\/i>.<\/li>\r\n \t<li>Obtain a [latex](1 - \\alpha) \\times 100%[\/latex] confidence interval for the difference between two population proportions [latex](p_1 - p_2)[\/latex].<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>","rendered":"<h2><strong>Overview<\/strong><\/h2>\n<p>Chapters 8 and 9 introduced inferences for population means. This chapter focuses on inferences for another population parameter: <strong>the population proportion <em>p<\/em><\/strong>, defined as the proportion (or percentage) of a population with a specified attribute. For example, the proportion of times that athletes wearing blue uniforms win a judo match, the proportion of customers who respond to an advertisement, and the proportion of women who have arthritis.<\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>As a result of completing this chapter, you will be able to do the following:<\/p>\n<ul>\n<li>Explain why the sample proportion [latex]\\hat{p} = \\frac{x}{n}[\/latex] is a special type of sample mean [latex]\\bar{x} = \\frac{\\sum x_i}{n}[\/latex].<\/li>\n<li>Describe the sampling distribution of the sample proportion [latex]\\hat{p}[\/latex].<\/li>\n<li>Conduct a one-proportion <i>z-test<\/i>.<\/li>\n<li>Obtain a [latex](1 - \\alpha) \\times 100%[\/latex] confidence interval for the population proportion [latex]p[\/latex].<\/li>\n<li>Describe the sampling distribution of the difference between two sample proportions [latex](\\hat{p}_1 - \\hat{p}_2)[\/latex].<\/li>\n<li>Conduct a two-proportion <i>z-test<\/i>.<\/li>\n<li>Obtain a [latex](1 - \\alpha) \\times 100%[\/latex] confidence interval for the difference between two population proportions [latex](p_1 - p_2)[\/latex].<\/li>\n<\/ul>\n<\/div>\n<\/div>\n","protected":false},"parent":0,"menu_order":10,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-1075","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1075","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":11,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1075\/revisions"}],"predecessor-version":[{"id":4855,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1075\/revisions\/4855"}],"wp:attachment":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/media?parent=1075"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/contributor?post=1075"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/license?post=1075"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}