{"id":4945,"date":"2022-08-17T00:39:45","date_gmt":"2022-08-17T00:39:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=4945"},"modified":"2022-08-17T18:56:29","modified_gmt":"2022-08-17T18:56:29","slug":"13c-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/13c-preview\/","title":{"raw":"13C Preview","rendered":"13C Preview"},"content":{"raw":"

Preparing for the next class\u00a0<\/strong><\/p>\r\nIn the next in-class activity, you will need to be able to apply the steps for a hypothesis\u00a0 test to compare two population means and compare results of a hypothesis test to the\u00a0 corresponding confidence interval using appropriate notation.\r\n

The Maternal Smoking Study\u00a0<\/strong><\/p>\r\nThere are many studies that link maternal smoking to lower birth weights, premature\u00a0 births, and miscarriages. Researchers in the early 1960s collected birth weights, dates,\u00a0 and gestational periods as part of the Child Health and Development Studies organization in 1961 and 1962. Information about the babies\u2019 parents\u2014age, education,\u00a0 height, weight, and whether the mother smoked\u2014was also recorded. The variables included in the dataset are:\r\n\r\ngestation: Length of gestation (in days)\r\n\r\nwt: Weight (in ounces)\r\n\r\nage: Mother's age in years at termination of pregnancy\r\n\r\nsmoke: Does mother smoke? (never, smokes now, until current pregnancy, once\u00a0 did, not now)\r\n\r\nsmoke_now: Does mother currently smoke?\r\n\r\n\u201cYes\u201d includes \u201csmokes now\u201d\r\n\r\n\u201cNo\" includes responses of \u201cuntil current pregnancy,\u201d \u201conce did,\u201d \u201cnot\u00a0 now,\u201d and \u201cnever.\u201d\r\n\r\nTen observations are presented in the following table. The full dataset is found in spreadsheet DCMP_STAT_13C_Maternal_Smoke.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
gestation<\/td>\r\nsmoke<\/td>\r\nsmoke_now<\/td>\r\nage<\/td>\r\nwt<\/td>\r\n<\/tr>\r\n
284<\/td>\r\nnever<\/td>\r\nNo<\/td>\r\n27<\/td>\r\n120<\/td>\r\n<\/tr>\r\n
282<\/td>\r\nnever<\/td>\r\nNo<\/td>\r\n33<\/td>\r\n113<\/td>\r\n<\/tr>\r\n
279<\/td>\r\nnow<\/td>\r\nYes<\/td>\r\n28<\/td>\r\n128<\/td>\r\n<\/tr>\r\n
282<\/td>\r\nnow<\/td>\r\nYes<\/td>\r\n23<\/td>\r\n108<\/td>\r\n<\/tr>\r\n
286<\/td>\r\nuntil current pregnancy<\/td>\r\nNo<\/td>\r\n25<\/td>\r\n136<\/td>\r\n<\/tr>\r\n
244<\/td>\r\nnever<\/td>\r\nNo<\/td>\r\n33<\/td>\r\n138<\/td>\r\n<\/tr>\r\n
245<\/td>\r\nnever<\/td>\r\nNo<\/td>\r\n23<\/td>\r\n132<\/td>\r\n<\/tr>\r\n
289<\/td>\r\nnever<\/td>\r\nNo<\/td>\r\n25<\/td>\r\n120<\/td>\r\n<\/tr>\r\n
299<\/td>\r\nnow<\/td>\r\nYes<\/td>\r\n30<\/td>\r\n143<\/td>\r\n<\/tr>\r\n
351<\/td>\r\nonce did, not now<\/td>\r\nNo<\/td>\r\n27<\/td>\r\n140<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n

Question 1<\/h3>\r\n1) Suppose we wanted to study the difference in birth weight of babies born to mothers\u00a0 who smoked during pregnancy (smoke_now = yes) and mothers who did not smoke\u00a0 during pregnancy.\r\n\r\na) Clearly define the two populations of interest.\r\n\r\nRecall that when we are interested in estimating a difference in population means,\u00a0 we usually start with data from a sample from each of the populations of interest.\r\n\r\nThere are two different strategies for selecting the two samples. One strategy is to select a sample from one population and then independently select a sample from\u00a0 the second population. Using this strategy results in two samples where the\u00a0 individuals selected for the first sample do not influence the individuals selected for\u00a0 the second sample.\r\n\r\nThis would be the case if you take a random sample from each population. Samples\u00a0 selected in this way are said to be independent samples.\r\n\r\nb) Can the samples defined in this study be considered independent? Explain.\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\n2) Using the DCMP Describing and Exploring Quantitative Variables \u2013 Several Groups tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/, describe the mean,\u00a0 standard deviation, and sample sizes for each group defined in Question 1.\r\n\r\nComplete the following table, which represents notation that we can use to help us\u00a0 distinguish the sample mean, standard deviation, and sample size for the subjects in\u00a0 Group 1 vs. the subjects in Group 2.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nGroup 1:\r\n\r\nsmoke_now = Yes\r\n\r\nMothers who\r\n\r\nsmoked during\r\n\r\npregnancy<\/td>\r\nGroup 2:\r\n\r\nsmoke_now = No\r\n\r\nMothers who did not\u00a0 smoke during\r\n\r\npregnancy<\/td>\r\n<\/tr>\r\n
Sample Mean<\/td>\r\n[latex]\\bar{x}_{1}=[\/latex] _____<\/td>\r\n[latex]\\bar{x}_{2}=[\/latex] _____<\/td>\r\n<\/tr>\r\n
Sample Standard\u00a0 Deviation<\/td>\r\n[latex]s_{1}=[\/latex] ______<\/td>\r\n[latex]s_{2}=[\/latex] ______<\/td>\r\n<\/tr>\r\n
Sample Size<\/td>\r\n[latex]n_{1}=[\/latex] _____<\/td>\r\n[latex]n_{1}=[\/latex] _____<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nHint: Use spreadsheet DCMP_STAT_13C_Maternal_Smoke!\r\n\r\n<\/div>\r\n
\r\n

Question 3<\/h3>\r\n3) One way to compare the means of two groups is by looking at the difference of the means.\r\n\r\na) Write an expression that represents the difference between the two sample\u00a0 means using the notation in the table you completed in Question 2.\r\n\r\nb) Write an expression to represent the difference between the population\u00a0 means.\r\n\r\nc) What would be the value of the difference between the population means if\u00a0 there was no difference between the groups?\r\n\r\nHint: If there was no difference between the population means, [latex]\\mu_{1}=\\mu_{2}[\/latex]. Think about\u00a0 the value you would get if you subtracted [latex]\\mu_{2}[\/latex] from[latex]\\mu_{1}[\/latex].\r\n\r\nd) Describe, in the context of the study, what it means if there was no difference between the two groups.\r\n\r\n<\/div>\r\nWhen we are interested in estimating a difference in population means using data from\u00a0 independent samples, we will use a two-sample t confidence interval (In-Class Activity\u00a0 12.D) or a two-sample t-test.\r\n\r\nThe conditions that you need to check for the two-sample t-test are the same as a two sample t confidence interval, presented in Preview Assignment 12.D:\r\n
    \r\n \t
  1. The samples are independent.<\/li>\r\n \t
  2. Each sample is a random sample from the corresponding population of interest\u00a0 or it is reasonable to regard the sample as random. It is reasonable to regard the\u00a0 sample as a random sample if it was selected in a way that should result in a\u00a0 sample that is representative of the population. If the data are from an\u00a0 experiment, we just need to check that there was random assignment to\u00a0 experimental groups\u2014this substitutes for the random sample condition\u00a0 and also results in independent samples.<\/li>\r\n \t
  3. For each population, the distribution of the variable that was measured is\u00a0 approximately normal, or the sample size for the sample from that population is\u00a0 large. Usually, a sample of size 30 or more is considered to be \u201clarge.\u201d If a\u00a0 sample size is less than 30, you should look at a plot of the data from that\u00a0 sample (a dotplot, a boxplot, or, if the sample size isn\u2019t really small, a histogram)\u00a0 to make sure that the distribution looks approximately symmetric and that there\u00a0 are no outliers.<\/li>\r\n<\/ol>\r\n
    \r\n

    Question 4<\/h3>\r\n4) Does the maternal smoking study satisfy the conditions for a two-sample t-test?\r\n\r\n<\/div>\r\n
    \r\n

    Question 5<\/h3>\r\n5) We can use a hypothesis test to determine if the observed difference in sample\u00a0 means is consistent with a hypothesized difference in population means.\r\n\r\nTo do this, we use what we know about the sampling distribution of [latex]\\bar{x}_{1}-\\bar{x}_{2}[\/latex] and, in particular, its estimated standard deviation (the standard error). Recall from In-Class\u00a0 Activity 12.D that you learned that the difference in the sample means, [latex]\\bar{x}_{1}-\\bar{x}_{2}[\/latex], also has an approximately normal distribution, centered at the difference of the population means, [latex]\\bar{x}_{1}-\\bar{x}_{2}[\/latex]. The standard deviation is given by the following formula:\r\n

    [latex]\\sqrt{\\frac{\\sigma^{2}_{1}}{n_{1}}+\\frac{\\sigma^{2}_{2}}{n_{2}}}[\/latex]<\/p>\r\nIn practice, we will have to estimate the standard deviation because it depends on\u00a0 the unknown population standard deviations. Replacing [latex]\\sigma_{1}[\/latex] and [latex]\\sigma_{2}[\/latex] by the sample standard deviations [latex]s_{1}[\/latex] and [latex]s_{2}[\/latex], we get the standard error<\/strong> of the difference:\r\n\r\n[latex]standard\\;error\\;of\\;\\bar{x}_{1}-\\bar{x}_{2}=\\sqrt{\\frac{s^{2}_{1}}{n_{1}}+\\frac{s^{2}_{2}}{n_{2}}}[\/latex]\r\n\r\na) Calculate the estimated difference in the means in Question 2.\r\n\r\nb) Calculate the standard error for the distribution using the statistics from Question 2. Round your answer to the nearest hundredth.\r\n\r\nHint: Use the formula [latex]SE=\\sqrt{\\frac{s^{2}_{1}}{n_{1}}+\\frac{s^{2}_{2}}{n_{2}}}[\/latex]\r\n\r\nc) Interpret the meaning of this value.\r\n\r\n<\/div>\r\n

    \r\n

    Question 6<\/h3>\r\n6) Use the DCMP Describing and Exploring Quantitative Variables \u2013 Several Groups tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/ to visualize the\u00a0 difference in means between the two groups defined in Question 2 using histograms.\r\n\r\n<\/div>\r\n
    \r\n

    Question 7<\/h3>\r\n7) Briefly describe the difference (or lack thereof) between the two groups. Do you think\u00a0 there is a significant difference between the birth weights of babies born to mothers\u00a0 who smoked during pregnancy versus those who did not? Be prepared to share your\u00a0 conclusions in class.\r\n\r\n<\/div>\r\nThis analysis uses descriptive statistics only. How can we make an inference about the\u00a0 difference when the population refers to all pregnant women? We will answer this\u00a0 question in the next in-class activity.","rendered":"

    Preparing for the next class\u00a0<\/strong><\/p>\n

    In the next in-class activity, you will need to be able to apply the steps for a hypothesis\u00a0 test to compare two population means and compare results of a hypothesis test to the\u00a0 corresponding confidence interval using appropriate notation.<\/p>\n

    The Maternal Smoking Study\u00a0<\/strong><\/p>\n

    There are many studies that link maternal smoking to lower birth weights, premature\u00a0 births, and miscarriages. Researchers in the early 1960s collected birth weights, dates,\u00a0 and gestational periods as part of the Child Health and Development Studies organization in 1961 and 1962. Information about the babies\u2019 parents\u2014age, education,\u00a0 height, weight, and whether the mother smoked\u2014was also recorded. The variables included in the dataset are:<\/p>\n

    gestation: Length of gestation (in days)<\/p>\n

    wt: Weight (in ounces)<\/p>\n

    age: Mother’s age in years at termination of pregnancy<\/p>\n

    smoke: Does mother smoke? (never, smokes now, until current pregnancy, once\u00a0 did, not now)<\/p>\n

    smoke_now: Does mother currently smoke?<\/p>\n

    \u201cYes\u201d includes \u201csmokes now\u201d<\/p>\n

    \u201cNo” includes responses of \u201cuntil current pregnancy,\u201d \u201conce did,\u201d \u201cnot\u00a0 now,\u201d and \u201cnever.\u201d<\/p>\n

    Ten observations are presented in the following table. The full dataset is found in spreadsheet DCMP_STAT_13C_Maternal_Smoke.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
    gestation<\/td>\nsmoke<\/td>\nsmoke_now<\/td>\nage<\/td>\nwt<\/td>\n<\/tr>\n
    284<\/td>\nnever<\/td>\nNo<\/td>\n27<\/td>\n120<\/td>\n<\/tr>\n
    282<\/td>\nnever<\/td>\nNo<\/td>\n33<\/td>\n113<\/td>\n<\/tr>\n
    279<\/td>\nnow<\/td>\nYes<\/td>\n28<\/td>\n128<\/td>\n<\/tr>\n
    282<\/td>\nnow<\/td>\nYes<\/td>\n23<\/td>\n108<\/td>\n<\/tr>\n
    286<\/td>\nuntil current pregnancy<\/td>\nNo<\/td>\n25<\/td>\n136<\/td>\n<\/tr>\n
    244<\/td>\nnever<\/td>\nNo<\/td>\n33<\/td>\n138<\/td>\n<\/tr>\n
    245<\/td>\nnever<\/td>\nNo<\/td>\n23<\/td>\n132<\/td>\n<\/tr>\n
    289<\/td>\nnever<\/td>\nNo<\/td>\n25<\/td>\n120<\/td>\n<\/tr>\n
    299<\/td>\nnow<\/td>\nYes<\/td>\n30<\/td>\n143<\/td>\n<\/tr>\n
    351<\/td>\nonce did, not now<\/td>\nNo<\/td>\n27<\/td>\n140<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
    \n

    Question 1<\/h3>\n

    1) Suppose we wanted to study the difference in birth weight of babies born to mothers\u00a0 who smoked during pregnancy (smoke_now = yes) and mothers who did not smoke\u00a0 during pregnancy.<\/p>\n

    a) Clearly define the two populations of interest.<\/p>\n

    Recall that when we are interested in estimating a difference in population means,\u00a0 we usually start with data from a sample from each of the populations of interest.<\/p>\n

    There are two different strategies for selecting the two samples. One strategy is to select a sample from one population and then independently select a sample from\u00a0 the second population. Using this strategy results in two samples where the\u00a0 individuals selected for the first sample do not influence the individuals selected for\u00a0 the second sample.<\/p>\n

    This would be the case if you take a random sample from each population. Samples\u00a0 selected in this way are said to be independent samples.<\/p>\n

    b) Can the samples defined in this study be considered independent? Explain.<\/p>\n<\/div>\n

    \n

    Question 2<\/h3>\n

    2) Using the DCMP Describing and Exploring Quantitative Variables \u2013 Several Groups tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/, describe the mean,\u00a0 standard deviation, and sample sizes for each group defined in Question 1.<\/p>\n

    Complete the following table, which represents notation that we can use to help us\u00a0 distinguish the sample mean, standard deviation, and sample size for the subjects in\u00a0 Group 1 vs. the subjects in Group 2.<\/p>\n

    \n\n\n\n\n\n\n
    <\/td>\nGroup 1:<\/p>\n

    smoke_now = Yes<\/p>\n

    Mothers who<\/p>\n

    smoked during<\/p>\n

    pregnancy<\/td>\n

    		Group 2:<\/p>\n

    smoke_now = No<\/p>\n

    Mothers who did not\u00a0 smoke during<\/p>\n

    pregnancy<\/td>\n<\/tr>\n

    Sample Mean<\/td>\n[latex]\\bar{x}_{1}=[\/latex] _____<\/td>\n[latex]\\bar{x}_{2}=[\/latex] _____<\/td>\n<\/tr>\n
    Sample Standard\u00a0 Deviation<\/td>\n[latex]s_{1}=[\/latex] ______<\/td>\n[latex]s_{2}=[\/latex] ______<\/td>\n<\/tr>\n
    Sample Size<\/td>\n[latex]n_{1}=[\/latex] _____<\/td>\n[latex]n_{1}=[\/latex] _____<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    Hint: Use spreadsheet DCMP_STAT_13C_Maternal_Smoke!<\/p>\n<\/div>\n

    \n

    Question 3<\/h3>\n

    3) One way to compare the means of two groups is by looking at the difference of the means.<\/p>\n

    a) Write an expression that represents the difference between the two sample\u00a0 means using the notation in the table you completed in Question 2.<\/p>\n

    b) Write an expression to represent the difference between the population\u00a0 means.<\/p>\n

    c) What would be the value of the difference between the population means if\u00a0 there was no difference between the groups?<\/p>\n

    Hint: If there was no difference between the population means, [latex]\\mu_{1}=\\mu_{2}[\/latex]. Think about\u00a0 the value you would get if you subtracted [latex]\\mu_{2}[\/latex] from[latex]\\mu_{1}[\/latex].<\/p>\n

    d) Describe, in the context of the study, what it means if there was no difference between the two groups.<\/p>\n<\/div>\n

    When we are interested in estimating a difference in population means using data from\u00a0 independent samples, we will use a two-sample t confidence interval (In-Class Activity\u00a0 12.D) or a two-sample t-test.<\/p>\n

    The conditions that you need to check for the two-sample t-test are the same as a two sample t confidence interval, presented in Preview Assignment 12.D:<\/p>\n

      \n
    1. The samples are independent.<\/li>\n
    2. Each sample is a random sample from the corresponding population of interest\u00a0 or it is reasonable to regard the sample as random. It is reasonable to regard the\u00a0 sample as a random sample if it was selected in a way that should result in a\u00a0 sample that is representative of the population. If the data are from an\u00a0 experiment, we just need to check that there was random assignment to\u00a0 experimental groups\u2014this substitutes for the random sample condition\u00a0 and also results in independent samples.<\/li>\n
    3. For each population, the distribution of the variable that was measured is\u00a0 approximately normal, or the sample size for the sample from that population is\u00a0 large. Usually, a sample of size 30 or more is considered to be \u201clarge.\u201d If a\u00a0 sample size is less than 30, you should look at a plot of the data from that\u00a0 sample (a dotplot, a boxplot, or, if the sample size isn\u2019t really small, a histogram)\u00a0 to make sure that the distribution looks approximately symmetric and that there\u00a0 are no outliers.<\/li>\n<\/ol>\n
      \n

      Question 4<\/h3>\n

      4) Does the maternal smoking study satisfy the conditions for a two-sample t-test?<\/p>\n<\/div>\n

      \n

      Question 5<\/h3>\n

      5) We can use a hypothesis test to determine if the observed difference in sample\u00a0 means is consistent with a hypothesized difference in population means.<\/p>\n

      To do this, we use what we know about the sampling distribution of [latex]\\bar{x}_{1}-\\bar{x}_{2}[\/latex] and, in particular, its estimated standard deviation (the standard error). Recall from In-Class\u00a0 Activity 12.D that you learned that the difference in the sample means, [latex]\\bar{x}_{1}-\\bar{x}_{2}[\/latex], also has an approximately normal distribution, centered at the difference of the population means, [latex]\\bar{x}_{1}-\\bar{x}_{2}[\/latex]. The standard deviation is given by the following formula:<\/p>\n

      [latex]\\sqrt{\\frac{\\sigma^{2}_{1}}{n_{1}}+\\frac{\\sigma^{2}_{2}}{n_{2}}}[\/latex]<\/p>\n

      In practice, we will have to estimate the standard deviation because it depends on\u00a0 the unknown population standard deviations. Replacing [latex]\\sigma_{1}[\/latex] and [latex]\\sigma_{2}[\/latex] by the sample standard deviations [latex]s_{1}[\/latex] and [latex]s_{2}[\/latex], we get the standard error<\/strong> of the difference:<\/p>\n

      [latex]standard\\;error\\;of\\;\\bar{x}_{1}-\\bar{x}_{2}=\\sqrt{\\frac{s^{2}_{1}}{n_{1}}+\\frac{s^{2}_{2}}{n_{2}}}[\/latex]<\/p>\n

      a) Calculate the estimated difference in the means in Question 2.<\/p>\n

      b) Calculate the standard error for the distribution using the statistics from Question 2. Round your answer to the nearest hundredth.<\/p>\n

      Hint: Use the formula [latex]SE=\\sqrt{\\frac{s^{2}_{1}}{n_{1}}+\\frac{s^{2}_{2}}{n_{2}}}[\/latex]<\/p>\n

      c) Interpret the meaning of this value.<\/p>\n<\/div>\n

      \n

      Question 6<\/h3>\n

      6) Use the DCMP Describing and Exploring Quantitative Variables \u2013 Several Groups tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/ to visualize the\u00a0 difference in means between the two groups defined in Question 2 using histograms.<\/p>\n<\/div>\n

      \n

      Question 7<\/h3>\n

      7) Briefly describe the difference (or lack thereof) between the two groups. Do you think\u00a0 there is a significant difference between the birth weights of babies born to mothers\u00a0 who smoked during pregnancy versus those who did not? Be prepared to share your\u00a0 conclusions in class.<\/p>\n<\/div>\n

      This analysis uses descriptive statistics only. How can we make an inference about the\u00a0 difference when the population refers to all pregnant women? We will answer this\u00a0 question in the next in-class activity.<\/p>\n","protected":false},"author":23592,"menu_order":9,"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-4945","chapter","type-chapter","status-publish","hentry"],"part":4875,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4945","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\/23592"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4945\/revisions"}],"predecessor-version":[{"id":4947,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4945\/revisions\/4947"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4875"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4945\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4945"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4945"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4945"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}