{"id":5366,"date":"2022-08-19T23:04:38","date_gmt":"2022-08-19T23:04:38","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=5366"},"modified":"2022-08-20T19:38:07","modified_gmt":"2022-08-20T19:38:07","slug":"11d-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/11d-preview\/","title":{"raw":"11D Preview","rendered":"11D Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to be able to conduct a complete hypothesis\u00a0 test for a proportion and write the conclusion of a hypothesis test in context. You will\u00a0 also need to understand that there are limitations on P-values and verify that the\u00a0 conditions of the one-sample z-test for proportions have been met.\r\n\r\nIn the previous in-class activity, you learned that a P-value is a probability that\u00a0 measures the likelihood of observing a test statistic at least as extreme as the one\u00a0 observed (in the direction of the alternative hypothesis). Also, recall that once a P-value\u00a0 is calculated, we compare it to the significance level in order to decide whether we have\u00a0 enough evidence to reject the null hypothesis in favor of the alternative hypothesis.\r\n\r\nUltimately, when we calculate and use the P-value, the goal is to arrive at the conclusion of a hypothesis test. Once we decide whether we have enough evidence to\u00a0 reject a null hypothesis, we write a statement in context of the original question asked in\u00a0 order to describe the outcome of the hypothesis test. It is important to remember that\u00a0 we never prove that a null hypothesis is true; we only conclude that the sample data\u00a0 collected either do or do not support the alternative hypothesis. Therefore, one of two\u00a0 statements will be concluded, as presented in the table below.\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Decision<\/td>\r\n<td>Conclusion<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>If P-value [latex] \\leq \\alpha [\/latex], there is enough evidence to reject the null hypothesis.<\/td>\r\n<td>At the\u00a0[latex] \\alpha [\/latex] \u00d7 100% significance level, the\u00a0 data provide convincing evidence in\u00a0 support of the alternative hypothesis.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>If P-value\u00a0 [latex] &gt; \\alpha [\/latex] there is not enough\u00a0 evidence to reject the null hypothesis.<\/td>\r\n<td>At the\u00a0[latex] \\alpha [\/latex] \u00d7 100% significance level, the\u00a0 data do not provide convincing evidence\u00a0 in support of the alternative hypothesis.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 1<\/h3>\r\nAccording to a 2003 Pew Research study, 70% of college students reported playing video games.[footnote]Jones, S. (2003, July 6). <em>Gaming comes of age<\/em>. Pew Research Center. https:\/\/www.pewresearch.org\/internet\/2003\/07\/06\/gaming-comes-of-age\/[\/footnote] A researcher wonders if more than 70% of college students play video games today. She collects data from a random sample of college students. Consider the hypotheses:\r\n\r\n[latex] H_{0}:p = 0.7H_{A}:p &gt; 0.7 [\/latex]\r\n\r\nBased on her sample, she obtains a test statistic and a P-value of 0.024.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Is there reason to reject the null hypothesis at a 5% significance level?\u00a0 Explain.\r\nHint: Recall the rejection rule: If the P-value is less than or equal to [latex] \\alpha [\/latex], reject the null\u00a0 hypothesis.<\/li>\r\n \t<li>Fill in the blank with either \u201cdo\u201d or \u201cdo not.\u201d\r\nAt the 5% significance level, the data _____ provide convincing evidence\u00a0 that more than 70% of college students play video games.<\/li>\r\n \t<li>Is there reason to reject the null hypothesis at a 1% significance level?\u00a0 Explain.\r\nHint: Recall the rejection rule: If the P-value is less than or equal to [latex] \\alpha [\/latex], reject the null\u00a0 hypothesis.<\/li>\r\n \t<li>Fill in the blank with either \u201cdo\u201d or \u201cdo not.\u201d\r\nAt the 1% significance level, the data _____ provide convincing evidence\u00a0 that more than 70% of college students play video games.<\/li>\r\n<\/ol>\r\n<\/div>\r\nTo summarize, in order to conduct a hypothesis test, you need to do the following:\r\n<div class=\"textbox\">\r\n\r\nOne-Sample Z-Test of Proportions *MISSING LATEX*\r\n<ul>\r\n \t<li aria-level=\"1\">Write out the null and alternative hypotheses.<\/li>\r\n \t<li aria-level=\"1\">Check the conditions for the hypothesis test. For testing a one-sample z-test for proportions, we require:\r\n<ul>\r\n \t<li aria-level=\"2\">Large Counts: Check that\u00a0 10 and\u00a0 10.<\/li>\r\n \t<li aria-level=\"2\">Random Samples\/Assignment: Check that the sample is a random sample.<\/li>\r\n \t<li aria-level=\"2\">10% Population Size: Check that the sample size, , is less than 10% of the population size, :\u00a0 0.10.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Calculate a test statistic.<\/li>\r\n \t<li aria-level=\"1\">Calculate a P-value.<\/li>\r\n \t<li aria-level=\"1\">Compare the P-value to the significance level to make a decision.<\/li>\r\n \t<li aria-level=\"1\">Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 2<\/h3>\r\nA student reads a headline claiming \u201c20% of college students in the United States\u00a0 have student loans.\u201d She believes the percentage of students in the United States who have student loans is much higher. She polls 15 of her friends and asks them\u00a0 \u201cDo you have student loans?\u201d She wants to prove at the 1% significance level that\u00a0 the percentage of students in the United States who have student loans is higher\u00a0 than 20%. Are the conditions of the one-sample z-test for proportions met?\r\n\r\nHint: Check the three conditions for the one-sample proportion z-test.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 3<\/h3>\r\nA <em>Statista<\/em> Global Consumer Survey reports that approximately 20% of people in Nigeria say they own some type of cryptocurrency, such as Bitcoin, Ethereum, or\u00a0 Dogecoin.[footnote] Buchholz, K. (2021, March 17). <em>How common is crypto?<\/em> Statista. https:\/\/www.statista.com\/chart\/18345\/crypto-currency-adoption\/[\/footnote] A researcher in the United States believes to have observed hesitancy of\u00a0 Americans to purchase cryptocurrency. He obtains a random sample of 850\u00a0 Americans and asks if they have purchased cryptocurrency. Of those surveyed, 142 replied that they have. At the 5% significance level, do the data provide convincing\u00a0 evidence that the proportion of Americans buying cryptocurrency is less than what is\u00a0 reported in Nigeria?\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Write the null hypothesis using the appropriate symbolic notation.<\/li>\r\n \t<li>Write the alternative hypothesis using the appropriate symbolic notation.<\/li>\r\n \t<li>Verify the conditions of the one-sample z-test for proportions.\r\nHint: There are three conditions to check. Remember that\u00a0[latex] p [\/latex] is the null hypothesized\u00a0 value for the large count condition.<\/li>\r\n \t<li>Calculate the test statistic using the DCMP Inference for Population\u00a0 Proportion tool that was introduced for confidence intervals in In-Class\u00a0 Activity 10.D.\r\n<ul>\r\n \t<li aria-level=\"1\">Go to <a href=\"https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/\">https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/<\/a>.<\/li>\r\n \t<li aria-level=\"1\">Under \u201cEnter Data,\u201d select \u201cNumber of Successes.\u201d<\/li>\r\n \t<li aria-level=\"1\">Enter \u201cSample Size\u201d and \u201c# of Successes.\u201d<\/li>\r\n \t<li aria-level=\"1\">Add appropriate labels for success and failure by selecting \u201cSuccess\/Failure.\u201d<\/li>\r\n \t<li aria-level=\"1\">Under \u201cType of Inference,\u201d select \u201cSignificance Test.\u201d<\/li>\r\n \t<li aria-level=\"1\">Enter the \u201cNull Value of [latex] p_{0} [\/latex].\u201d This is the hypothesized value in the null hypothesis.<\/li>\r\n \t<li aria-level=\"1\">Select the appropriate \u201cAlternative\u201d given your alternative hypothesis.<\/li>\r\n \t<li aria-level=\"1\">Remember that:\r\n<ul>\r\n \t<li aria-level=\"2\">\u201cTwo-sided\u201d corresponds to [latex] H_{A}: p \\neq p_{0}[\/latex].<\/li>\r\n \t<li aria-level=\"2\">\u201cLess\u201d corresponds to [latex] H_{A}: p &lt; p_{0} [\/latex].<\/li>\r\n \t<li aria-level=\"2\">\u201cGreater\u201d corresponds to [latex] H_{A}: p &gt; p_{0} [\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>What is the P-value?\r\nHint: Remember that you have a lower-tailed test.<\/li>\r\n \t<li>Will the null hypothesis be rejected? Explain.<\/li>\r\n \t<li>At the 5% significance level, do the data provide convincing evidence that the proportion of Americans buying cryptocurrency is less than what is reported in Nigeria? Write the conclusion in a sentence.<\/li>\r\n<\/ol>\r\n<\/div>\r\nA note on P-values: Though P-values are widely used, there are some limitations on their use and significant debate as to their reliability. Recall that a P-value is calculated based on one sample of data collected, and, as a result, it may be difficult to obtain a similar P-value upon replication of an experiment. Additionally, P-values can be manipulated by increased sample size. In some studies, instead of using a P-value to answer the binary question (\u201cIs there or is there not statistical significance?\u201d), it may be better to consider the effect size which answers the question \u201cHow strong is the effect in the sample?\u201d For example, in reporting the effect size, a researcher explains by how much a treatment works rather than just if it works. Additionally, in using effect sizes, quantitative comparisons between the results of different studies can be made.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 4<\/h3>\r\nDetermine whether this statement is true or false: A P-value explains how strong an effect is in a sample of data.\r\n\r\n<\/div>\r\nLooking ahead\r\n\r\nIn the next class, you will be revisiting the results of a research study done at Virginia Tech to analyze the condition of plumbing in Flint, Michigan. Over the last several years, Flint, Michigan has been in the news because of contaminated water. To get a better idea of what has occurred in Flint, Michigan, visit <a href=\"https:\/\/www.nrdc.org\/stories\/flint-water-crisis-everything-you-need-know\">https:\/\/www.nrdc.org\/stories\/flint-water-crisis-everything-you-need-know<\/a>. Read about the problems that have occurred because of lead-contaminated water here: <a href=\"https:\/\/www.nrdc.org\/stories\/flint-water-crisis-everything-you-need-know#sec-whyis\">https:\/\/www.nrdc.org\/stories\/flint-water-crisis-everything-you-need-know#sec-whyis<\/a>.\r\n\r\nYou should be able to:\r\n<ul>\r\n \t<li aria-level=\"1\">Briefly describe the situation.<\/li>\r\n \t<li aria-level=\"1\">Identify effects of drinking lead-contaminated water.<\/li>\r\n<\/ul>\r\n<\/div>","rendered":"<p>Preparing for the next class<\/p>\n<p>In the next in-class activity, you will need to be able to conduct a complete hypothesis\u00a0 test for a proportion and write the conclusion of a hypothesis test in context. You will\u00a0 also need to understand that there are limitations on P-values and verify that the\u00a0 conditions of the one-sample z-test for proportions have been met.<\/p>\n<p>In the previous in-class activity, you learned that a P-value is a probability that\u00a0 measures the likelihood of observing a test statistic at least as extreme as the one\u00a0 observed (in the direction of the alternative hypothesis). Also, recall that once a P-value\u00a0 is calculated, we compare it to the significance level in order to decide whether we have\u00a0 enough evidence to reject the null hypothesis in favor of the alternative hypothesis.<\/p>\n<p>Ultimately, when we calculate and use the P-value, the goal is to arrive at the conclusion of a hypothesis test. Once we decide whether we have enough evidence to\u00a0 reject a null hypothesis, we write a statement in context of the original question asked in\u00a0 order to describe the outcome of the hypothesis test. It is important to remember that\u00a0 we never prove that a null hypothesis is true; we only conclude that the sample data\u00a0 collected either do or do not support the alternative hypothesis. Therefore, one of two\u00a0 statements will be concluded, as presented in the table below.<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<td>Decision<\/td>\n<td>Conclusion<\/td>\n<\/tr>\n<tr>\n<td>If P-value [latex]\\leq \\alpha[\/latex], there is enough evidence to reject the null hypothesis.<\/td>\n<td>At the\u00a0[latex]\\alpha[\/latex] \u00d7 100% significance level, the\u00a0 data provide convincing evidence in\u00a0 support of the alternative hypothesis.<\/td>\n<\/tr>\n<tr>\n<td>If P-value\u00a0 [latex]> \\alpha[\/latex] there is not enough\u00a0 evidence to reject the null hypothesis.<\/td>\n<td>At the\u00a0[latex]\\alpha[\/latex] \u00d7 100% significance level, the\u00a0 data do not provide convincing evidence\u00a0 in support of the alternative hypothesis.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox key-takeaways\">\n<h3>Question 1<\/h3>\n<p>According to a 2003 Pew Research study, 70% of college students reported playing video games.<a class=\"footnote\" title=\"Jones, S. (2003, July 6). Gaming comes of age. Pew Research Center. https:\/\/www.pewresearch.org\/internet\/2003\/07\/06\/gaming-comes-of-age\/\" id=\"return-footnote-5366-1\" href=\"#footnote-5366-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> A researcher wonders if more than 70% of college students play video games today. She collects data from a random sample of college students. Consider the hypotheses:<\/p>\n<p>[latex]H_{0}:p = 0.7H_{A}:p > 0.7[\/latex]<\/p>\n<p>Based on her sample, she obtains a test statistic and a P-value of 0.024.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Is there reason to reject the null hypothesis at a 5% significance level?\u00a0 Explain.<br \/>\nHint: Recall the rejection rule: If the P-value is less than or equal to [latex]\\alpha[\/latex], reject the null\u00a0 hypothesis.<\/li>\n<li>Fill in the blank with either \u201cdo\u201d or \u201cdo not.\u201d<br \/>\nAt the 5% significance level, the data _____ provide convincing evidence\u00a0 that more than 70% of college students play video games.<\/li>\n<li>Is there reason to reject the null hypothesis at a 1% significance level?\u00a0 Explain.<br \/>\nHint: Recall the rejection rule: If the P-value is less than or equal to [latex]\\alpha[\/latex], reject the null\u00a0 hypothesis.<\/li>\n<li>Fill in the blank with either \u201cdo\u201d or \u201cdo not.\u201d<br \/>\nAt the 1% significance level, the data _____ provide convincing evidence\u00a0 that more than 70% of college students play video games.<\/li>\n<\/ol>\n<\/div>\n<p>To summarize, in order to conduct a hypothesis test, you need to do the following:<\/p>\n<div class=\"textbox\">\n<p>One-Sample Z-Test of Proportions *MISSING LATEX*<\/p>\n<ul>\n<li aria-level=\"1\">Write out the null and alternative hypotheses.<\/li>\n<li aria-level=\"1\">Check the conditions for the hypothesis test. For testing a one-sample z-test for proportions, we require:\n<ul>\n<li aria-level=\"2\">Large Counts: Check that\u00a0 10 and\u00a0 10.<\/li>\n<li aria-level=\"2\">Random Samples\/Assignment: Check that the sample is a random sample.<\/li>\n<li aria-level=\"2\">10% Population Size: Check that the sample size, , is less than 10% of the population size, :\u00a0 0.10.<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Calculate a test statistic.<\/li>\n<li aria-level=\"1\">Calculate a P-value.<\/li>\n<li aria-level=\"1\">Compare the P-value to the significance level to make a decision.<\/li>\n<li aria-level=\"1\">Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 2<\/h3>\n<p>A student reads a headline claiming \u201c20% of college students in the United States\u00a0 have student loans.\u201d She believes the percentage of students in the United States who have student loans is much higher. She polls 15 of her friends and asks them\u00a0 \u201cDo you have student loans?\u201d She wants to prove at the 1% significance level that\u00a0 the percentage of students in the United States who have student loans is higher\u00a0 than 20%. Are the conditions of the one-sample z-test for proportions met?<\/p>\n<p>Hint: Check the three conditions for the one-sample proportion z-test.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 3<\/h3>\n<p>A <em>Statista<\/em> Global Consumer Survey reports that approximately 20% of people in Nigeria say they own some type of cryptocurrency, such as Bitcoin, Ethereum, or\u00a0 Dogecoin.<a class=\"footnote\" title=\"Buchholz, K. (2021, March 17). How common is crypto? Statista. https:\/\/www.statista.com\/chart\/18345\/crypto-currency-adoption\/\" id=\"return-footnote-5366-2\" href=\"#footnote-5366-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a> A researcher in the United States believes to have observed hesitancy of\u00a0 Americans to purchase cryptocurrency. He obtains a random sample of 850\u00a0 Americans and asks if they have purchased cryptocurrency. Of those surveyed, 142 replied that they have. At the 5% significance level, do the data provide convincing\u00a0 evidence that the proportion of Americans buying cryptocurrency is less than what is\u00a0 reported in Nigeria?<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Write the null hypothesis using the appropriate symbolic notation.<\/li>\n<li>Write the alternative hypothesis using the appropriate symbolic notation.<\/li>\n<li>Verify the conditions of the one-sample z-test for proportions.<br \/>\nHint: There are three conditions to check. Remember that\u00a0[latex]p[\/latex] is the null hypothesized\u00a0 value for the large count condition.<\/li>\n<li>Calculate the test statistic using the DCMP Inference for Population\u00a0 Proportion tool that was introduced for confidence intervals in In-Class\u00a0 Activity 10.D.\n<ul>\n<li aria-level=\"1\">Go to <a href=\"https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/\">https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/<\/a>.<\/li>\n<li aria-level=\"1\">Under \u201cEnter Data,\u201d select \u201cNumber of Successes.\u201d<\/li>\n<li aria-level=\"1\">Enter \u201cSample Size\u201d and \u201c# of Successes.\u201d<\/li>\n<li aria-level=\"1\">Add appropriate labels for success and failure by selecting \u201cSuccess\/Failure.\u201d<\/li>\n<li aria-level=\"1\">Under \u201cType of Inference,\u201d select \u201cSignificance Test.\u201d<\/li>\n<li aria-level=\"1\">Enter the \u201cNull Value of [latex]p_{0}[\/latex].\u201d This is the hypothesized value in the null hypothesis.<\/li>\n<li aria-level=\"1\">Select the appropriate \u201cAlternative\u201d given your alternative hypothesis.<\/li>\n<li aria-level=\"1\">Remember that:\n<ul>\n<li aria-level=\"2\">\u201cTwo-sided\u201d corresponds to [latex]H_{A}: p \\neq p_{0}[\/latex].<\/li>\n<li aria-level=\"2\">\u201cLess\u201d corresponds to [latex]H_{A}: p < p_{0}[\/latex].<\/li>\n<li aria-level=\"2\">\u201cGreater\u201d corresponds to [latex]H_{A}: p > p_{0}[\/latex].<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>What is the P-value?<br \/>\nHint: Remember that you have a lower-tailed test.<\/li>\n<li>Will the null hypothesis be rejected? Explain.<\/li>\n<li>At the 5% significance level, do the data provide convincing evidence that the proportion of Americans buying cryptocurrency is less than what is reported in Nigeria? Write the conclusion in a sentence.<\/li>\n<\/ol>\n<\/div>\n<p>A note on P-values: Though P-values are widely used, there are some limitations on their use and significant debate as to their reliability. Recall that a P-value is calculated based on one sample of data collected, and, as a result, it may be difficult to obtain a similar P-value upon replication of an experiment. Additionally, P-values can be manipulated by increased sample size. In some studies, instead of using a P-value to answer the binary question (\u201cIs there or is there not statistical significance?\u201d), it may be better to consider the effect size which answers the question \u201cHow strong is the effect in the sample?\u201d For example, in reporting the effect size, a researcher explains by how much a treatment works rather than just if it works. Additionally, in using effect sizes, quantitative comparisons between the results of different studies can be made.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 4<\/h3>\n<p>Determine whether this statement is true or false: A P-value explains how strong an effect is in a sample of data.<\/p>\n<\/div>\n<p>Looking ahead<\/p>\n<p>In the next class, you will be revisiting the results of a research study done at Virginia Tech to analyze the condition of plumbing in Flint, Michigan. Over the last several years, Flint, Michigan has been in the news because of contaminated water. To get a better idea of what has occurred in Flint, Michigan, visit <a href=\"https:\/\/www.nrdc.org\/stories\/flint-water-crisis-everything-you-need-know\">https:\/\/www.nrdc.org\/stories\/flint-water-crisis-everything-you-need-know<\/a>. Read about the problems that have occurred because of lead-contaminated water here: <a href=\"https:\/\/www.nrdc.org\/stories\/flint-water-crisis-everything-you-need-know#sec-whyis\">https:\/\/www.nrdc.org\/stories\/flint-water-crisis-everything-you-need-know#sec-whyis<\/a>.<\/p>\n<p>You should be able to:<\/p>\n<ul>\n<li aria-level=\"1\">Briefly describe the situation.<\/li>\n<li aria-level=\"1\">Identify effects of drinking lead-contaminated water.<\/li>\n<\/ul>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-5366-1\">Jones, S. (2003, July 6). <em>Gaming comes of age<\/em>. Pew Research Center. https:\/\/www.pewresearch.org\/internet\/2003\/07\/06\/gaming-comes-of-age\/ <a href=\"#return-footnote-5366-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-5366-2\"> Buchholz, K. (2021, March 17). <em>How common is crypto?<\/em> Statista. https:\/\/www.statista.com\/chart\/18345\/crypto-currency-adoption\/ <a href=\"#return-footnote-5366-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":12,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5366","chapter","type-chapter","status-publish","hentry"],"part":5305,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5366","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/574340"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5366\/revisions"}],"predecessor-version":[{"id":5369,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5366\/revisions\/5369"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5305"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5366\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5366"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5366"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5366"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}