{"id":4969,"date":"2022-08-17T16:36:33","date_gmt":"2022-08-17T16:36:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=4969"},"modified":"2022-08-17T17:09:49","modified_gmt":"2022-08-17T17:09:49","slug":"7c-in-class-activity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/7c-in-class-activity\/","title":{"raw":"7C In-Class Activity","rendered":"7C In-Class Activity"},"content":{"raw":"
\r\n

Question 1<\/h3>\r\nAnswer the following questions with a partner:\r\n
    \r\n \t
  1. If it is snowing, what is the probability someone will ride their bike?<\/li>\r\n \t
  2. If you know someone holds one\u00a0\u00a0political belief, how likely are they to hold a conflicting political belief?\r\n\"\"\r\nCredit: iStock\/FatCamera<\/li>\r\n<\/ol>\r\n<\/div>\r\nThe General Social Survey (GSS) is a project of the independent research organization\u00a0 NORC at the University of Chicago, with principal funding from the National Science\u00a0 Foundation.[footnote]About GSS Data Explorer.<\/em> (n.d.). GSS Data Explorer. Retrieved from gssdataexplorer.norc.org[\/footnote]\r\n\r\nIn 2018, the GSS asked survey respondents whether the United States\u2019 spending on\u00a0 alternative energy was too little, about right, or too much. Similarly, respondents were\u00a0 also asked whether the United States\u2019 spending on childcare was too little, about right,\u00a0 or too much. The following table shows the data.\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    <\/td>\r\nChildcare Assistance<\/td>\r\n<\/tr>\r\n
    Too Little<\/td>\r\nAbout\r\n\r\nRight<\/td>\r\nToo\r\n\r\nMuch<\/td>\r\nTOTAL<\/td>\r\n<\/tr>\r\n
    Developing\u00a0 Alternative\r\n\r\nEnergy\r\n\r\nResources<\/td>\r\nToo Little<\/td>\r\n783<\/td>\r\n369<\/td>\r\n47<\/td>\r\n1,199<\/td>\r\n<\/tr>\r\n
    About Right<\/td>\r\n418<\/td>\r\n297<\/td>\r\n41<\/td>\r\n756<\/td>\r\n<\/tr>\r\n
    Too Much<\/td>\r\n78<\/td>\r\n54<\/td>\r\n32<\/td>\r\n164<\/td>\r\n<\/tr>\r\n
    TOTAL<\/td>\r\n1,279<\/td>\r\n720<\/td>\r\n120<\/td>\r\n2,199<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
    \r\n

    Question 2<\/h3>\r\nUse the table to estimate the following probabilities:\r\n
      \r\n \t
    1. The probability that a person thinks the United States spends too much on childcare<\/li>\r\n \t
    2. The probability that a person thinks the United States spends about the right\u00a0 amount on both childcare and developing alternative energy resources<\/li>\r\n \t
    3. The probability that a person thinks the United States spends about the right\u00a0 amount developing alternative energy resources and too much on childcare<\/li>\r\n<\/ol>\r\n<\/div>\r\n
      \r\n

      Question 3<\/h3>\r\nThe previous questions asked about people in general, so the denominator was the\u00a0 total number of people in the survey (2,199). Now, let\u2019s focus on the people who\u00a0 think the United States spends too little on childcare.\r\n
        \r\n \t
      1. What is the new denominator if we focus on the people who think the United\u00a0 States spends too little on childcare?<\/li>\r\n \t
      2. What is the probability that a person believes the United States spends too\u00a0 little on developing alternative energy resources GIVEN they think the United\u00a0 States spends too little on childcare?<\/li>\r\n<\/ol>\r\n<\/div>\r\n
        \r\n

        Question 4<\/h3>\r\nUse the previous table to estimate the following conditional probabilities:\r\n
          \r\n \t
        1. The probability that a randomly selected person thinks the United States spends too much on childcare GIVEN they think the United States spends\u00a0 about the right amount developing alternative energy resources<\/li>\r\n \t
        2. The probability that a randomly selected person thinks the United States spends about the right amount developing alternative energy resources\u00a0 GIVEN they think the United States spends too much on childcare<\/li>\r\n<\/ol>\r\n<\/div>\r\n
          \r\n

          Question 5<\/h3>\r\nEvery day, Jade recorded whether she drank bubble tea, caf\u00e9 sua da, both, or\u00a0 neither. On 5% of days, she drank both bubble tea and caf\u00e9 sua da. On 35% of\u00a0 days, she drank caf\u00e9 sua da and did not drink bubble tea. On 20% of days, Jade\u00a0 drank bubble tea. On 80% of days, Jade did not drink bubble tea.\r\n
            \r\n \t
          1. Assume Jade\u2019s data are from the last 100 days. This means she drank both\u00a0 caf\u00e9 sua da and bubble tea on 0.05 * 100 = 5 days. Use this information to\u00a0 complete the following table.\r\n
            \r\n\r\n\r\n\r\n\r\n\r\n\r\n
            <\/td>\r\nDrinks bubble tea<\/td>\r\nDoes not drink\r\n\r\nbubble tea<\/td>\r\nTotal<\/td>\r\n<\/tr>\r\n
            Drinks caf\u00e9 sua da<\/td>\r\n5<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
            Does not drink\r\n\r\ncaf\u00e9 sua da<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
            Total<\/td>\r\n20<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div><\/li>\r\n \t
          2. The probability of Jade not drinking bubble tea on a randomly selected day\u00a0 is [latex] \\frac{(35+45)}{100} = 0.80 [\/latex], or 80%. What is the probability of Jade drinking\u00a0 bubble tea on a given day?<\/li>\r\n \t
          3. On a randomly selected day, what is the probability that Jade drinks\u00a0 caf\u00e9 sua da?<\/li>\r\n \t
          4. What is the probability of Jade drinking bubble tea AND caf\u00e9 sua da on the\u00a0 same randomly selected day?<\/li>\r\n \t
          5. What is the probability of Jade drinking bubble tea GIVEN she drank caf\u00e9\u00a0 sua da?\r\n
            \r\n\r\nFormula for Conditional Probability\r\nFor any events A and B where [latex] P(B) > 0 [\/latex],\r\n\r\n[latex] P(A GIVEN B) = \\frac{P(A AND B)}{P(B)} [\/latex]\r\n\r\n<\/div>\r\n <\/li>\r\n \t
          6. Use the formula above to check your answer to Part E.\r\nRecall that two events are independent if [latex] P(A) GIVEN B) = P(A). [\/latex]\r\nAlternatively, two events are independent if [latex] P(A) * P(B) = P(A AND B). [\/latex]<\/li>\r\n \t
          7. Can we say that these two events\u2014drinking bubble tea and drinking\u00a0 caf\u00e9 sua da\u2014are independent? Explain.<\/li>\r\n \t
          8. Can we say that these two events\u2014drinking bubble tea and drinking\u00a0 caf\u00e9 sua da\u2014are independent? Explain.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
            \r\n

            Question 6<\/h3>\r\nConsider two events A and B with [latex] P(A) > 0 [\/latex] and [latex] P(B) > 0 [\/latex]. Can A and B be both\u00a0 mutually exclusive AND independent? Explain.\r\n\r\n<\/div>\r\n ","rendered":"
            \n

            Question 1<\/h3>\n

            Answer the following questions with a partner:<\/p>\n

              \n
            1. If it is snowing, what is the probability someone will ride their bike?<\/li>\n
            2. If you know someone holds one\u00a0\u00a0political belief, how likely are they to hold a conflicting political belief?
              \n\"\"
              \nCredit: iStock\/FatCamera<\/li>\n<\/ol>\n<\/div>\n

              The General Social Survey (GSS) is a project of the independent research organization\u00a0 NORC at the University of Chicago, with principal funding from the National Science\u00a0 Foundation.[1]<\/sup><\/a><\/p>\n

              In 2018, the GSS asked survey respondents whether the United States\u2019 spending on\u00a0 alternative energy was too little, about right, or too much. Similarly, respondents were\u00a0 also asked whether the United States\u2019 spending on childcare was too little, about right,\u00a0 or too much. The following table shows the data.<\/p>\n

              \n\n\n\n\n\n\n\n\n
              <\/td>\nChildcare Assistance<\/td>\n<\/tr>\n
              Too Little<\/td>\nAbout<\/p>\n

              Right<\/td>\n

              		Too<\/p>\n

              Much<\/td>\n

              		TOTAL<\/td>\n<\/tr>\n
              Developing\u00a0 Alternative<\/p>\n

              Energy<\/p>\n

              Resources<\/td>\n

              		Too Little<\/td>\n783<\/td>\n369<\/td>\n47<\/td>\n1,199<\/td>\n<\/tr>\n
              About Right<\/td>\n418<\/td>\n297<\/td>\n41<\/td>\n756<\/td>\n<\/tr>\n
              Too Much<\/td>\n78<\/td>\n54<\/td>\n32<\/td>\n164<\/td>\n<\/tr>\n
              TOTAL<\/td>\n1,279<\/td>\n720<\/td>\n120<\/td>\n2,199<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
              \n

              Question 2<\/h3>\n

              Use the table to estimate the following probabilities:<\/p>\n

                \n
              1. The probability that a person thinks the United States spends too much on childcare<\/li>\n
              2. The probability that a person thinks the United States spends about the right\u00a0 amount on both childcare and developing alternative energy resources<\/li>\n
              3. The probability that a person thinks the United States spends about the right\u00a0 amount developing alternative energy resources and too much on childcare<\/li>\n<\/ol>\n<\/div>\n
                \n

                Question 3<\/h3>\n

                The previous questions asked about people in general, so the denominator was the\u00a0 total number of people in the survey (2,199). Now, let\u2019s focus on the people who\u00a0 think the United States spends too little on childcare.<\/p>\n

                  \n
                1. What is the new denominator if we focus on the people who think the United\u00a0 States spends too little on childcare?<\/li>\n
                2. What is the probability that a person believes the United States spends too\u00a0 little on developing alternative energy resources GIVEN they think the United\u00a0 States spends too little on childcare?<\/li>\n<\/ol>\n<\/div>\n
                  \n

                  Question 4<\/h3>\n

                  Use the previous table to estimate the following conditional probabilities:<\/p>\n

                    \n
                  1. The probability that a randomly selected person thinks the United States spends too much on childcare GIVEN they think the United States spends\u00a0 about the right amount developing alternative energy resources<\/li>\n
                  2. The probability that a randomly selected person thinks the United States spends about the right amount developing alternative energy resources\u00a0 GIVEN they think the United States spends too much on childcare<\/li>\n<\/ol>\n<\/div>\n
                    \n

                    Question 5<\/h3>\n

                    Every day, Jade recorded whether she drank bubble tea, caf\u00e9 sua da, both, or\u00a0 neither. On 5% of days, she drank both bubble tea and caf\u00e9 sua da. On 35% of\u00a0 days, she drank caf\u00e9 sua da and did not drink bubble tea. On 20% of days, Jade\u00a0 drank bubble tea. On 80% of days, Jade did not drink bubble tea.<\/p>\n

                      \n
                    1. Assume Jade\u2019s data are from the last 100 days. This means she drank both\u00a0 caf\u00e9 sua da and bubble tea on 0.05 * 100 = 5 days. Use this information to\u00a0 complete the following table.\n
                      \n\n\n\n\n\n\n
                      <\/td>\nDrinks bubble tea<\/td>\nDoes not drink<\/p>\n

                      bubble tea<\/td>\n

                      		Total<\/td>\n<\/tr>\n
                      Drinks caf\u00e9 sua da<\/td>\n5<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                      Does not drink<\/p>\n

                      caf\u00e9 sua da<\/td>\n

                      		<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                      Total<\/td>\n20<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/li>\n
                    2. The probability of Jade not drinking bubble tea on a randomly selected day\u00a0 is [latex]\\frac{(35+45)}{100} = 0.80[\/latex], or 80%. What is the probability of Jade drinking\u00a0 bubble tea on a given day?<\/li>\n
                    3. On a randomly selected day, what is the probability that Jade drinks\u00a0 caf\u00e9 sua da?<\/li>\n
                    4. What is the probability of Jade drinking bubble tea AND caf\u00e9 sua da on the\u00a0 same randomly selected day?<\/li>\n
                    5. What is the probability of Jade drinking bubble tea GIVEN she drank caf\u00e9\u00a0 sua da?\n
                      \n

                      Formula for Conditional Probability
                      \nFor any events A and B where [latex]P(B) > 0[\/latex],<\/p>\n

                      [latex]P(A GIVEN B) = \\frac{P(A AND B)}{P(B)}[\/latex]<\/p>\n<\/div>\n

                       <\/li>\n

                    6. Use the formula above to check your answer to Part E.
                      \nRecall that two events are independent if [latex]P(A) GIVEN B) = P(A).[\/latex]
                      \nAlternatively, two events are independent if [latex]P(A) * P(B) = P(A AND B).[\/latex]<\/li>\n
                    7. Can we say that these two events\u2014drinking bubble tea and drinking\u00a0 caf\u00e9 sua da\u2014are independent? Explain.<\/li>\n
                    8. Can we say that these two events\u2014drinking bubble tea and drinking\u00a0 caf\u00e9 sua da\u2014are independent? Explain.<\/li>\n<\/ol>\n<\/div>\n
                      \n

                      Question 6<\/h3>\n

                      Consider two events A and B with [latex]P(A) > 0[\/latex] and [latex]P(B) > 0[\/latex]. Can A and B be both\u00a0 mutually exclusive AND independent? Explain.<\/p>\n<\/div>\n

                       <\/p>\n

                      1. About GSS Data Explorer.<\/em> (n.d.). GSS Data Explorer. Retrieved from gssdataexplorer.norc.org ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"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-4969","chapter","type-chapter","status-publish","hentry"],"part":4871,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4969","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":9,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4969\/revisions"}],"predecessor-version":[{"id":4990,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4969\/revisions\/4990"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4871"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4969\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4969"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4969"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4969"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}