{"id":4885,"date":"2022-08-16T17:41:19","date_gmt":"2022-08-16T17:41:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=4885"},"modified":"2022-08-17T18:20:37","modified_gmt":"2022-08-17T18:20:37","slug":"13a-inclass","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/13a-inclass\/","title":{"raw":"13A InClass","rendered":"13A InClass"},"content":{"raw":"
\r\n

Question 1<\/h3>\r\n1) Which corporations from around the\u00a0world do you think contribute the most to\u00a0polluting our environment with plastic\u00a0waste?\r\n\r\n<\/div>\r\n\r\n[caption id=\"\" align=\"alignright\" width=\"300\"]\"A Credit: iStock\/piotr_malczyk[\/caption]\r\n\r\nIn Questions 2\u20139, you will use a dataset called \u201cplastics.\u201d This dataset is a sample of\u00a0 plastic products collected by community volunteers in countries around the world during\u00a0 a brand audit to see what types of plastics are found in waste and from which\u00a0 companies the plastics found came from.\r\n\r\nThe dataset can be accessed here:\r\n\r\nhttps:\/\/docs.google.com\/spreadsheets\/d\/15RIs8K9MaGVfYQmi15bH87dUIz8X1o60Wcs ukoLlFFo\/edit?usp=sharing.\r\n\r\nThe dataset variables and variable descriptions are provided in the following table.\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\r\n\r\n\r\n\r\n\r\n
Variable<\/td>\r\nDescription<\/td>\r\n<\/tr>\r\n
country<\/td>\r\nCountry of cleanup<\/td>\r\n<\/tr>\r\n
year<\/td>\r\nYear (2019 or 2020)<\/td>\r\n<\/tr>\r\n
parent_company<\/td>\r\nSource of plastic<\/td>\r\n<\/tr>\r\n
empty<\/td>\r\nCategory left empty count<\/td>\r\n<\/tr>\r\n
hdpe<\/td>\r\nHigh-density polyethylene count (plastic milk\u00a0 containers, plastic bags, bottle caps, trash cans, oil\u00a0 cans, plastic lumber, toolboxes, supplement\u00a0 containers)<\/td>\r\n<\/tr>\r\n
Idpe<\/td>\r\nLow-density polyethylene count (plastic bags,\u00a0 Ziploc bags, buckets, squeeze bottles, plastic\u00a0 tubes, chopping boards)<\/td>\r\n<\/tr>\r\n
other_count<\/td>\r\nCategory marked other count<\/td>\r\n<\/tr>\r\n
pet<\/td>\r\nPolyester plastic count (polyester fibers, soft drink\u00a0 bottles, food containers [also see plastic bottles])<\/td>\r\n<\/tr>\r\n
pp<\/td>\r\nPolypropylene count (flower pots, bumpers, car\u00a0 interior trim, industrial fibers, carry-out beverage\u00a0 cups, microwavable food containers, DVD cases)<\/td>\r\n<\/tr>\r\n
ps<\/td>\r\nPolystyrene count (toys, video cassettes, ashtrays,\u00a0 trunks, beverage\/food coolers, beer cups, wine and\u00a0 champagne cups, carry-out food containers,\u00a0 styrofoam)<\/td>\r\n<\/tr>\r\n
pvc<\/td>\r\nPVC plastic count (window frames, bottles for\u00a0 chemicals, flooring, plumbing pipes)<\/td>\r\n<\/tr>\r\n
grand_total<\/td>\r\nGrand total count (all types of plastic)<\/td>\r\n<\/tr>\r\n
num_events<\/td>\r\nNumber of counting events<\/td>\r\n<\/tr>\r\n
volunteers<\/td>\r\nNumber of volunteers<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\n2) Plastic items contain recycling codes that appear within a chasing arrow logo like the one shown here:\"A\r\nWhat do you think these codes mean?\r\n\r\n<\/div>\r\n
\r\n

Question 3<\/h3>\r\n3) Looking at the \u201cplastics\u201d dataset, how many different types of plastic are represented\u00a0 in the dataset? List the different types.\r\n\r\n<\/div>\r\n \r\n
\r\n

Question 4<\/h3>\r\n4) Use the following dashboard website that has the \u201cplastics\u201d dataset loaded:\u00a0 https:\/\/sarahsauve.shinyapps.io\/TidyTuesdayBrandAuditDashboard\/.\r\n\r\nSelect a country that interests you from the drop-down menu at the top of the #breakfreefromplastic dashboard.\r\n\r\na) What are the total numbers of plastics recorded in 2019 and 2020 for that\u00a0 country?\r\n\r\nb) Are there any companies reported as top polluters in 2019 or 2020 for that\u00a0 country? If so, what is the top company and what is the % of recorded\u00a0 plastics?\r\n\r\n<\/div>\r\n \r\n\r\nIn Questions 5\u20138, you will use a subset of the \u201cplastics\u201d dataset. This subset contains all\u00a0 of the countries from the original data that have counts of plastics from The Coca-Cola\u00a0 Company in 2020. To create the subset, go to the \u201cplastics\u201d dataset and complete the following steps:\r\n
    \r\n \t
  1. Highlight the top row.<\/li>\r\n \t
  2. Select \u201cData.\u201d<\/li>\r\n \t
  3. Select \u201cFilter views.\u201d<\/li>\r\n \t
  4. Select \u201cCreate new temporary filter view.\u201d<\/li>\r\n<\/ol>\r\nNow, filter the data using parent_company = \u201cThe Coca-Cola Company\u201d and year =\u00a0 \u201c2020.\u201d If filtered correctly, the number of observations in the dataset should be [latex]n[\/latex] = 50,\u00a0 and the first few observations should look like this:\r\n\r\n[caption id=\"attachment_1974\" align=\"alignnone\" width=\"950\"]\"\" NO ALT TEXT[\/caption]\r\n\r\n
    \r\n

    Question 5<\/h3>\r\n5) We are interested in answering the following research question about the \u201cplastics\u201d dataset:\r\n\r\n\u201cFor the products reported from The Coca-Cola Company, is the average total\u00a0 plastics count found in various countries in 2020 different from the claimed value of\u00a0 275 items for The Coca-Cola Company?\u201d\r\n\r\na) Based on the research question, are we interested in testing a proportion or\u00a0 a mean?\r\n\r\nRemember that for confidence intervals, if the population standard deviation is not\u00a0 known, the confidence intervals are based on the t Distribution rather than the\u00a0 normal distribution.\r\n\r\nb) What distribution do you think would be used in a hypothesis test that would\u00a0 answer this research question?\r\n\r\nc) Why should that type of distribution be used?\r\n\r\nd) Is this a one-sample or two-sample test?\r\n\r\n<\/div>\r\nRecall from In-Class Activity 12.B:\r\n
    \r\n\r\n\r\n\r\n
    t Distribution<\/strong>\r\n\r\nWhen taking many, many random samples of size [latex]n[\/latex] from a population distribution with mean [latex]\\mu[\/latex] and standard deviation [latex]\\sigma[\/latex], the t-statistic\r\n\r\n[latex]t=\\frac{\\bar{x}-\\mu}{SE(\\bar{x})}=\\frac{\\bar{x}-\\mu}{s\/\\sqrt{n}}[\/latex]\r\n\r\nwill follow a t Distribution with\r\n\r\n[latex]n-1[\/latex] degrees of freedom if:\r\n\r\n1. the population distribution is normal; or\r\n\r\n2. the population distribution is not too skewed and the sample size is large (e.g., [latex]n[\/latex] \u2265 30).<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nAs was the case with previous inference methods, there are a few assumptions\/conditions that you should check before using the one-sample t-test.\r\n\r\nConditions for a One-Sample t-Test<\/strong>\r\n
      \r\n \t
    1. The sample is a random sample<\/strong> from the population of interest or it is reasonable\u00a0 to regard the sample as if it is random. It is reasonable to regard the sample as a\u00a0 random sample if it was selected in a way that should result in a sample that is\u00a0 representative of the population.<\/li>\r\n \t
    2. For each population, the distribution of the variable that was measured is\u00a0approximately normal, or the sample size for the sample from that\u00a0 population is large<\/strong>. Usually, a sample of size 30 or more is considered to be\u00a0 \u201clarge.\u201d If a sample size is less than 30, you should look at a plot of the data from\u00a0 that sample (a dotplot, a boxplot, or, if the sample size isn\u2019t really small, a\u00a0 histogram) to make sure that the distribution looks approximately symmetric and\u00a0 that there are no outliers.<\/li>\r\n<\/ol>\r\n
      \r\n

      Question 6<\/h3>\r\n6) Create a histogram of the grand totals of all plastics found in various countries in\u00a0 2020 for The Coca-Cola Company using the DCMP Describing and Exploring\u00a0 Quantitative Variables tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/. Describe the shape and spread of the histogram. Note that a random sample of\u00a0 countries was taken each year, and the actual countries included varied from year to\u00a0 year.\r\n\r\n<\/div>\r\n
      \r\n

      Question 7<\/h3>\r\n7) Verify the conditions are met for a one-sample t-test.\r\n\r\na) Are the data a random sample from the population of interest? Is this\u00a0 condition met? Explain.\r\n\r\nb) Is the distribution of the variable total plastic counts approximately normal, or\u00a0 is the sample size for the sample from that population large? Is this condition met? Explain.\r\n\r\n<\/div>\r\n
      \r\n

      Question 8<\/h3>\r\n8) Write out the null and alternative hypotheses that would be used to answer the\u00a0 research question stated in Question 5. Remember to use the correct notation.\r\n\r\n<\/div>\r\n
      \r\n

      Question 9<\/h3>\r\n9) What if we are interested in answering the following question using samples from the\u00a0 \u201cplastics\u201d dataset:\r\n\r\n\u201cFor the products reported from The Coca-Cola Company, is the average total\u00a0 plastics count found in various countries in 2020 less than the average total plastics\u00a0 count from 2019?\u201d\r\n\r\na) Is this a one-sample or two-sample test?\r\n\r\nb) Write the null and alternative hypotheses that would be used to answer the\u00a0 research question. Define the parameters of interest using the correct\u00a0 notation, using [latex]\\mu_{1}[\/latex]to represent the population mean for total plastics for The\u00a0 Coca-Cola Company in 2019 and [latex]\\mu_{2}[\/latex] to represent the population mean for\u00a0 total plastics for The Coca-Cola Company in 2020.\r\n\r\n<\/div>","rendered":"
      \n

      Question 1<\/h3>\n

      1) Which corporations from around the\u00a0world do you think contribute the most to\u00a0polluting our environment with plastic\u00a0waste?<\/p>\n<\/div>\n

      \"A<\/p>\n

      Credit: iStock\/piotr_malczyk<\/p>\n<\/div>\n

      In Questions 2\u20139, you will use a dataset called \u201cplastics.\u201d This dataset is a sample of\u00a0 plastic products collected by community volunteers in countries around the world during\u00a0 a brand audit to see what types of plastics are found in waste and from which\u00a0 companies the plastics found came from.<\/p>\n

      The dataset can be accessed here:<\/p>\n

      https:\/\/docs.google.com\/spreadsheets\/d\/15RIs8K9MaGVfYQmi15bH87dUIz8X1o60Wcs ukoLlFFo\/edit?usp=sharing.<\/p>\n

      The dataset variables and variable descriptions are provided in the following table.<\/p>\n

      \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
      Variable<\/td>\nDescription<\/td>\n<\/tr>\n
      country<\/td>\nCountry of cleanup<\/td>\n<\/tr>\n
      year<\/td>\nYear (2019 or 2020)<\/td>\n<\/tr>\n
      parent_company<\/td>\nSource of plastic<\/td>\n<\/tr>\n
      empty<\/td>\nCategory left empty count<\/td>\n<\/tr>\n
      hdpe<\/td>\nHigh-density polyethylene count (plastic milk\u00a0 containers, plastic bags, bottle caps, trash cans, oil\u00a0 cans, plastic lumber, toolboxes, supplement\u00a0 containers)<\/td>\n<\/tr>\n
      Idpe<\/td>\nLow-density polyethylene count (plastic bags,\u00a0 Ziploc bags, buckets, squeeze bottles, plastic\u00a0 tubes, chopping boards)<\/td>\n<\/tr>\n
      other_count<\/td>\nCategory marked other count<\/td>\n<\/tr>\n
      pet<\/td>\nPolyester plastic count (polyester fibers, soft drink\u00a0 bottles, food containers [also see plastic bottles])<\/td>\n<\/tr>\n
      pp<\/td>\nPolypropylene count (flower pots, bumpers, car\u00a0 interior trim, industrial fibers, carry-out beverage\u00a0 cups, microwavable food containers, DVD cases)<\/td>\n<\/tr>\n
      ps<\/td>\nPolystyrene count (toys, video cassettes, ashtrays,\u00a0 trunks, beverage\/food coolers, beer cups, wine and\u00a0 champagne cups, carry-out food containers,\u00a0 styrofoam)<\/td>\n<\/tr>\n
      pvc<\/td>\nPVC plastic count (window frames, bottles for\u00a0 chemicals, flooring, plumbing pipes)<\/td>\n<\/tr>\n
      grand_total<\/td>\nGrand total count (all types of plastic)<\/td>\n<\/tr>\n
      num_events<\/td>\nNumber of counting events<\/td>\n<\/tr>\n
      volunteers<\/td>\nNumber of volunteers<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
      \n

      Question 2<\/h3>\n

      2) Plastic items contain recycling codes that appear within a chasing arrow logo like the one shown here:\"A
      \nWhat do you think these codes mean?<\/p>\n<\/div>\n

      \n

      Question 3<\/h3>\n

      3) Looking at the \u201cplastics\u201d dataset, how many different types of plastic are represented\u00a0 in the dataset? List the different types.<\/p>\n<\/div>\n

       <\/p>\n

      \n

      Question 4<\/h3>\n

      4) Use the following dashboard website that has the \u201cplastics\u201d dataset loaded:\u00a0 https:\/\/sarahsauve.shinyapps.io\/TidyTuesdayBrandAuditDashboard\/.<\/p>\n

      Select a country that interests you from the drop-down menu at the top of the #breakfreefromplastic dashboard.<\/p>\n

      a) What are the total numbers of plastics recorded in 2019 and 2020 for that\u00a0 country?<\/p>\n

      b) Are there any companies reported as top polluters in 2019 or 2020 for that\u00a0 country? If so, what is the top company and what is the % of recorded\u00a0 plastics?<\/p>\n<\/div>\n

       <\/p>\n

      In Questions 5\u20138, you will use a subset of the \u201cplastics\u201d dataset. This subset contains all\u00a0 of the countries from the original data that have counts of plastics from The Coca-Cola\u00a0 Company in 2020. To create the subset, go to the \u201cplastics\u201d dataset and complete the following steps:<\/p>\n

        \n
      1. Highlight the top row.<\/li>\n
      2. Select \u201cData.\u201d<\/li>\n
      3. Select \u201cFilter views.\u201d<\/li>\n
      4. Select \u201cCreate new temporary filter view.\u201d<\/li>\n<\/ol>\n

        Now, filter the data using parent_company = \u201cThe Coca-Cola Company\u201d and year =\u00a0 \u201c2020.\u201d If filtered correctly, the number of observations in the dataset should be [latex]n[\/latex] = 50,\u00a0 and the first few observations should look like this:<\/p>\n

        \"\"<\/p>\n

        NO ALT TEXT<\/p>\n<\/div>\n

        \n

        Question 5<\/h3>\n

        5) We are interested in answering the following research question about the \u201cplastics\u201d dataset:<\/p>\n

        \u201cFor the products reported from The Coca-Cola Company, is the average total\u00a0 plastics count found in various countries in 2020 different from the claimed value of\u00a0 275 items for The Coca-Cola Company?\u201d<\/p>\n

        a) Based on the research question, are we interested in testing a proportion or\u00a0 a mean?<\/p>\n

        Remember that for confidence intervals, if the population standard deviation is not\u00a0 known, the confidence intervals are based on the t Distribution rather than the\u00a0 normal distribution.<\/p>\n

        b) What distribution do you think would be used in a hypothesis test that would\u00a0 answer this research question?<\/p>\n

        c) Why should that type of distribution be used?<\/p>\n

        d) Is this a one-sample or two-sample test?<\/p>\n<\/div>\n

        Recall from In-Class Activity 12.B:<\/p>\n

        \n\n\n\n
        t Distribution<\/strong><\/p>\n

        When taking many, many random samples of size [latex]n[\/latex] from a population distribution with mean [latex]\\mu[\/latex] and standard deviation [latex]\\sigma[\/latex], the t-statistic<\/p>\n

        [latex]t=\\frac{\\bar{x}-\\mu}{SE(\\bar{x})}=\\frac{\\bar{x}-\\mu}{s\/\\sqrt{n}}[\/latex]<\/p>\n

        will follow a t Distribution with<\/p>\n

        [latex]n-1[\/latex] degrees of freedom if:<\/p>\n

        1. the population distribution is normal; or<\/p>\n

        2. the population distribution is not too skewed and the sample size is large (e.g., [latex]n[\/latex] \u2265 30).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

        As was the case with previous inference methods, there are a few assumptions\/conditions that you should check before using the one-sample t-test.<\/p>\n

        Conditions for a One-Sample t-Test<\/strong><\/p>\n

          \n
        1. The sample is a random sample<\/strong> from the population of interest or it is reasonable\u00a0 to regard the sample as if it is random. It is reasonable to regard the sample as a\u00a0 random sample if it was selected in a way that should result in a sample that is\u00a0 representative of the population.<\/li>\n
        2. For each population, the distribution of the variable that was measured is\u00a0approximately normal, or the sample size for the sample from that\u00a0 population is large<\/strong>. Usually, a sample of size 30 or more is considered to be\u00a0 \u201clarge.\u201d If a sample size is less than 30, you should look at a plot of the data from\u00a0 that sample (a dotplot, a boxplot, or, if the sample size isn\u2019t really small, a\u00a0 histogram) to make sure that the distribution looks approximately symmetric and\u00a0 that there are no outliers.<\/li>\n<\/ol>\n
          \n

          Question 6<\/h3>\n

          6) Create a histogram of the grand totals of all plastics found in various countries in\u00a0 2020 for The Coca-Cola Company using the DCMP Describing and Exploring\u00a0 Quantitative Variables tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/. Describe the shape and spread of the histogram. Note that a random sample of\u00a0 countries was taken each year, and the actual countries included varied from year to\u00a0 year.<\/p>\n<\/div>\n

          \n

          Question 7<\/h3>\n

          7) Verify the conditions are met for a one-sample t-test.<\/p>\n

          a) Are the data a random sample from the population of interest? Is this\u00a0 condition met? Explain.<\/p>\n

          b) Is the distribution of the variable total plastic counts approximately normal, or\u00a0 is the sample size for the sample from that population large? Is this condition met? Explain.<\/p>\n<\/div>\n

          \n

          Question 8<\/h3>\n

          8) Write out the null and alternative hypotheses that would be used to answer the\u00a0 research question stated in Question 5. Remember to use the correct notation.<\/p>\n<\/div>\n

          \n

          Question 9<\/h3>\n

          9) What if we are interested in answering the following question using samples from the\u00a0 \u201cplastics\u201d dataset:<\/p>\n

          \u201cFor the products reported from The Coca-Cola Company, is the average total\u00a0 plastics count found in various countries in 2020 less than the average total plastics\u00a0 count from 2019?\u201d<\/p>\n

          a) Is this a one-sample or two-sample test?<\/p>\n

          b) Write the null and alternative hypotheses that would be used to answer the\u00a0 research question. Define the parameters of interest using the correct\u00a0 notation, using [latex]\\mu_{1}[\/latex]to represent the population mean for total plastics for The\u00a0 Coca-Cola Company in 2019 and [latex]\\mu_{2}[\/latex] to represent the population mean for\u00a0 total plastics for The Coca-Cola Company in 2020.<\/p>\n<\/div>\n","protected":false},"author":23592,"menu_order":2,"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-4885","chapter","type-chapter","status-publish","hentry"],"part":4875,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4885","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":7,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4885\/revisions"}],"predecessor-version":[{"id":5023,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4885\/revisions\/5023"}],"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\/4885\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4885"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4885"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4885"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4885"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}