{"id":5398,"date":"2022-08-20T21:43:35","date_gmt":"2022-08-20T21:43:35","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5398"},"modified":"2022-08-20T22:03:42","modified_gmt":"2022-08-20T22:03:42","slug":"11g-in-class-activity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/11g-in-class-activity\/","title":{"raw":"11G In-Class Activity","rendered":"11G In-Class Activity"},"content":{"raw":"Recall the 2004 study by two University of Chicago economists who wanted to test for\u00a0 labor market discrimination. The results, which we analyzed in the last in-class activity,\u00a0 are summarized in the following table:\r\n\r\n\"\"\r\n
\r\n

Question 1<\/h3>\r\nIn the previous in-class activity, we conducted a two-sample z-test for proportions to test if commonly-white names received a truly higher callback proportion than commonly-black names.\r\n\r\nWrite down the hypotheses we used for this test and write a brief explanation of what each hypothesis means:\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\nRecall that all the conditions for inference were met. The z-test statistic value was 4.23, and the P-value was very close to 0.\r\n\r\nWhat conclusion can we draw from these results? State your conclusion in context. Use significance level [latex]\\alpha = 0.05 [\/latex].\r\n\r\n<\/div>\r\n
\r\n

Question 3<\/h3>\r\nGo to the DCMP Compare Two Population Proportions tool at https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/<\/a>. Select the \u201cNumber of successes\u201d option and input the relevant data from the study. Under the type of inference section, select \u201cConfidence Interval\u201d and a 95% confidence level.\r\n
    \r\n \t
  1. Part A: What is the confidence interval?<\/li>\r\n \t
  2. Part B: What exactly is this interval estimating? One proportion? Two proportions? A\u00a0 combination of proportions? Explain.<\/li>\r\n \t
  3. Part C: Interpret your interval in the context of the study.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
    \r\n

    Question 4<\/h3>\r\nLook back at the hypotheses for your test and your conclusion. Then, look back at\u00a0 the confidence interval. Let\u2019s compare these results.\r\n
      \r\n \t
    1. Part A: Do the values in your interval support the hypothesis (null or alternative) that\u00a0 your significance test also supported? Explain.<\/li>\r\n \t
    2. Part B: If the interval contained the null value of 0, would it be consistent with the\u00a0 results of the significance test? Explain.<\/li>\r\n<\/ol>\r\n<\/div>\r\nConfidence intervals contain\u00a0a range of plausible estimates of the population parameter.\u00a0 We just considered the population parameter of the difference of proportions, [latex] p_{1} -p_{2} [\/latex], but these results can extend to a confidence interval for any parameter, including one proportion, [latex]p [\/latex].\r\n\r\nThe confidence intervals constructed in these activities were two-tailed, since z* is the point on the standard normal distribution such that the proportion of area under the curve between [latex] -z^{*} [\/latex] and [latex] +z^{*}[\/latex] is [latex] C [\/latex], the confidence level.\r\n\r\nThe two-tailed confidence intervals with a confidence level of\u00a0[latex]C [\/latex] correspond to two-tailed hypothesis tests with a significance level of [latex] 1-C[\/latex].\r\n\r\nFor example, a 95% confidence interval corresponds to a hypothesis test with a significance level of 5%, or [latex] \\alpha = 0.05[\/latex]. Similarly, a 99% confidence interval corresponds to a hypothesis test with a significance level of 1%, or [latex]\\alpha =0.01 [\/latex].\r\n
      \r\n

      Question 5<\/h3>\r\nLet\u2019s connect these results to a one-sample test of proportions. Imagine you are a\u00a0 pollster. You randomly sample people in your county and ask them about their\u00a0 political leanings. Based on your sample, you create the following 95% confidence\u00a0 interval for the proportion of county voters who are Republican: (49%, 52%).\r\n\r\nImagine you also conduct a hypothesis test with the following hypotheses: *MISSING LATEX\r\n
        \r\n \t
      1. Part A: If you were to conduct the hypothesis test, would it be safe to reject the null\u00a0 hypothesis and conclude that there is significant evidence that the proportion\u00a0 of county voters that are Republican is 50%? Explain.<\/li>\r\n \t
      2. Part B: In this context, which would provide more information: a hypothesis test or a\u00a0 confidence interval? Explain.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
        \r\n

        Question 6<\/h3>\r\nRecall the vaping effects example in In-Class Activity 11.E. The National Institute on\u00a0 Drug Abuse was interested in the effects of the 2020 pandemic on drug abuse in\u00a0 teens. In particular, they were interested in the changes in vaping usage between\u00a0 the pre-pandemic period and three months into the pandemic.\r\n\r\nBefore the pandemic, 24% of 582 12th graders reported that they had vaped nicotine\u00a0 in the past 30 days. Three months into the pandemic, 17% of 582 12th graders\u00a0 reported that they had vaped nicotine in the past 30 days. Which of the following\u00a0 provides more information in this context? Explain.\r\n
          \r\n \t
        1. a) Hypothesis test:<\/li>\r\n<\/ol>\r\nThe null hypothesis for the study was [latex] H_{0}: p =0.24 [\/latex] and the alternative hypothesis\u00a0 was [latex] H_{A}: p =0.24 [\/latex] . The test resulted in a P-value [latex] < 0.000 [\/latex] so we concluded there\u00a0 was sufficient evidence to conclude that the proportion of 12th graders who vaped\u00a0 within the last 30 days changed from the pre-pandemic period to three months\u00a0 into the pandemic.\r\n
            \r\n \t
          1. b) Confidence interval:<\/li>\r\n<\/ol>\r\nWe are 95% confident that the true proportion of 12th graders who vaped within\u00a0 the last 30 days is between 0.1396 and 0.2006.\r\n\r\n<\/div>\r\nTypically, the conclusion drawn from a two-tailed confidence interval is usually the same\u00a0 as the conclusion drawn from a two-tailed hypothesis test. If a confidence interval contains the hypothesized parameter, a hypothesis test at the 0.05 level will almost\u00a0 always fail to reject the null hypothesis. If the 95% confidence interval does not contain\u00a0 the hypothesized parameter, a hypothesis test at the 0.05 level will almost always reject\u00a0 the null hypothesis. While this does not always hold for tests of proportions, a\u00a0 confidence interval typically provides more information about reasonable values of the\u00a0 parameter.","rendered":"

            Recall the 2004 study by two University of Chicago economists who wanted to test for\u00a0 labor market discrimination. The results, which we analyzed in the last in-class activity,\u00a0 are summarized in the following table:<\/p>\n

            \"\"<\/p>\n

            \n

            Question 1<\/h3>\n

            In the previous in-class activity, we conducted a two-sample z-test for proportions to test if commonly-white names received a truly higher callback proportion than commonly-black names.<\/p>\n

            Write down the hypotheses we used for this test and write a brief explanation of what each hypothesis means:<\/p>\n<\/div>\n

            \n

            Question 2<\/h3>\n

            Recall that all the conditions for inference were met. The z-test statistic value was 4.23, and the P-value was very close to 0.<\/p>\n

            What conclusion can we draw from these results? State your conclusion in context. Use significance level [latex]\\alpha = 0.05[\/latex].<\/p>\n<\/div>\n

            \n

            Question 3<\/h3>\n

            Go to the DCMP Compare Two Population Proportions tool at https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/<\/a>. Select the \u201cNumber of successes\u201d option and input the relevant data from the study. Under the type of inference section, select \u201cConfidence Interval\u201d and a 95% confidence level.<\/p>\n

              \n
            1. Part A: What is the confidence interval?<\/li>\n
            2. Part B: What exactly is this interval estimating? One proportion? Two proportions? A\u00a0 combination of proportions? Explain.<\/li>\n
            3. Part C: Interpret your interval in the context of the study.<\/li>\n<\/ol>\n<\/div>\n
              \n

              Question 4<\/h3>\n

              Look back at the hypotheses for your test and your conclusion. Then, look back at\u00a0 the confidence interval. Let\u2019s compare these results.<\/p>\n

                \n
              1. Part A: Do the values in your interval support the hypothesis (null or alternative) that\u00a0 your significance test also supported? Explain.<\/li>\n
              2. Part B: If the interval contained the null value of 0, would it be consistent with the\u00a0 results of the significance test? Explain.<\/li>\n<\/ol>\n<\/div>\n

                Confidence intervals contain\u00a0a range of plausible estimates of the population parameter.\u00a0 We just considered the population parameter of the difference of proportions, [latex]p_{1} -p_{2}[\/latex], but these results can extend to a confidence interval for any parameter, including one proportion, [latex]p[\/latex].<\/p>\n

                The confidence intervals constructed in these activities were two-tailed, since z* is the point on the standard normal distribution such that the proportion of area under the curve between [latex]-z^{*}[\/latex] and [latex]+z^{*}[\/latex] is [latex]C[\/latex], the confidence level.<\/p>\n

                The two-tailed confidence intervals with a confidence level of\u00a0[latex]C[\/latex] correspond to two-tailed hypothesis tests with a significance level of [latex]1-C[\/latex].<\/p>\n

                For example, a 95% confidence interval corresponds to a hypothesis test with a significance level of 5%, or [latex]\\alpha = 0.05[\/latex]. Similarly, a 99% confidence interval corresponds to a hypothesis test with a significance level of 1%, or [latex]\\alpha =0.01[\/latex].<\/p>\n

                \n

                Question 5<\/h3>\n

                Let\u2019s connect these results to a one-sample test of proportions. Imagine you are a\u00a0 pollster. You randomly sample people in your county and ask them about their\u00a0 political leanings. Based on your sample, you create the following 95% confidence\u00a0 interval for the proportion of county voters who are Republican: (49%, 52%).<\/p>\n

                Imagine you also conduct a hypothesis test with the following hypotheses: *MISSING LATEX<\/p>\n

                  \n
                1. Part A: If you were to conduct the hypothesis test, would it be safe to reject the null\u00a0 hypothesis and conclude that there is significant evidence that the proportion\u00a0 of county voters that are Republican is 50%? Explain.<\/li>\n
                2. Part B: In this context, which would provide more information: a hypothesis test or a\u00a0 confidence interval? Explain.<\/li>\n<\/ol>\n<\/div>\n
                  \n

                  Question 6<\/h3>\n

                  Recall the vaping effects example in In-Class Activity 11.E. The National Institute on\u00a0 Drug Abuse was interested in the effects of the 2020 pandemic on drug abuse in\u00a0 teens. In particular, they were interested in the changes in vaping usage between\u00a0 the pre-pandemic period and three months into the pandemic.<\/p>\n

                  Before the pandemic, 24% of 582 12th graders reported that they had vaped nicotine\u00a0 in the past 30 days. Three months into the pandemic, 17% of 582 12th graders\u00a0 reported that they had vaped nicotine in the past 30 days. Which of the following\u00a0 provides more information in this context? Explain.<\/p>\n

                    \n
                  1. a) Hypothesis test:<\/li>\n<\/ol>\n

                    The null hypothesis for the study was [latex]H_{0}: p =0.24[\/latex] and the alternative hypothesis\u00a0 was [latex]H_{A}: p =0.24[\/latex] . The test resulted in a P-value [latex]< 0.000[\/latex] so we concluded there\u00a0 was sufficient evidence to conclude that the proportion of 12th graders who vaped\u00a0 within the last 30 days changed from the pre-pandemic period to three months\u00a0 into the pandemic.\n\n\n

                      \n
                    1. b) Confidence interval:<\/li>\n<\/ol>\n

                      We are 95% confident that the true proportion of 12th graders who vaped within\u00a0 the last 30 days is between 0.1396 and 0.2006.<\/p>\n<\/div>\n

                      Typically, the conclusion drawn from a two-tailed confidence interval is usually the same\u00a0 as the conclusion drawn from a two-tailed hypothesis test. If a confidence interval contains the hypothesized parameter, a hypothesis test at the 0.05 level will almost\u00a0 always fail to reject the null hypothesis. If the 95% confidence interval does not contain\u00a0 the hypothesized parameter, a hypothesis test at the 0.05 level will almost always reject\u00a0 the null hypothesis. While this does not always hold for tests of proportions, a\u00a0 confidence interval typically provides more information about reasonable values of the\u00a0 parameter.<\/p>\n","protected":false},"author":574340,"menu_order":20,"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-5398","chapter","type-chapter","status-publish","hentry"],"part":5305,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5398","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":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5398\/revisions"}],"predecessor-version":[{"id":5410,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5398\/revisions\/5410"}],"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\/5398\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5398"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5398"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5398"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}