{"id":1620,"date":"2022-01-19T01:08:26","date_gmt":"2022-01-19T01:08:26","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=1620"},"modified":"2022-02-08T20:04:30","modified_gmt":"2022-02-08T20:04:30","slug":"9b-9c","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/9b-9c\/","title":{"raw":"9B\/9C","rendered":"9B\/9C"},"content":{"raw":"<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Sample<\/td>\r\n<td>Sample Proportion<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Skill or Concept: I can . . .<\/td>\r\n<td>Questions to check your understanding<\/td>\r\n<td>Rating\r\nfrom 1 to 5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify whether a summary measure is a parameter or a statistic.<\/td>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Determine the appropriate type of plot for a given dataset.<\/td>\r\n<td>3, Part A<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simulate sample proportions of random samples of a given size from a population with known .<\/td>\r\n<td>4, 5<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Describe and interpret features of a sampling distribution of sample proportions.<\/td>\r\n<td>2\r\n\r\n3, Part B\r\n\r\n3, Part C\r\n\r\n4\u20136<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Calculate the standard deviation of a sample proportion.<\/td>\r\n<td>7<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<img class=\"alignnone wp-image-1621\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010722\/Picture741-300x200.jpg\" alt=\"A display showing a graph labeled &quot;Unemployment.&quot;\" width=\"1097\" height=\"731\" \/>A dis<img class=\"alignnone wp-image-1622\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010728\/Picture751-300x169.jpg\" alt=\"An illustration of various terms related to sampling and distribution. In the top left corner, there is a bubble labeled \u201cPopulation: U.S. Labor Force.\u201d Beneath this bubble is a bar chart titled \u201cPopulation Distribution.\u201d The bar chart is labeled \u201cEmployment Level\u201d on the x-axis and \u201cProportion\u201d on the y-axis. For \u201cEmployed,\u201d the count is approximately 0.85. For \u201cUnemployed,\u201d the count is approximately 0.15. Beneath this graph is a caption reading \u201cPopulation proportion that are unemployed: p = 0.15.\u201d From the bubble labeled \u201cPopulation: U.S. Labor Force,\u201d there are also several arrows pointing to other bubbles. Above them, there is text reading \u201cMany many random samples of size n = 50.\u201d The bubbles are labeled the following: \u201cp = 0.11,\u201d \u201cp = 0.12,\u201d \u201cp = 0.18,\u201d \u201cp = 0.16,\u201d \u201cp = 0.20,\u201d \u201cp = 0.22,\u201d \u201cp = 0.14,\u201d and \u201cp = 0.18.\u201d From the bubble labeled \u201cp = 0.12,\u201d there is a bar chart to the right titled \u201cSample Distribution.\u201d On the x-axis, it is labeled \u201cEmployment Level,\u201d and on the y-axis, it is labeled \u201cProportion.\u201d For \u201cEmployed,\u201d the proportion is approximately 0.88, while for \u201cUnemployed,\u201d the proportion is approximately 0.12. Each of the bubbles also has an arrow leading from it to a graph in the bottom righthand corner. This graph is titled \u201cSampling Distribution of Sample Proportion,\u201d with a subheading that reads \u201cMean = 0.15, Standard deviation = 0.0499 (10,000 simulations of samples of size n = 50).\u201d On the x-axis, the graph is labeled \u201cSample proportion p, and on the y-axis, the graph is labeled \u201cFrequency.\u201d The graph is a bar graph with a peak around approximately 0.14. There is a dot at approximately 0.15. Beneath this graph and the bubbles to its left, there is text that reads \u201cSample proportion that are unemployed: p (value varies from sample to sample).\u201d\" width=\"1022\" height=\"576\" \/> <img class=\"alignnone wp-image-1623\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010733\/Picture761-300x203.jpg\" alt=\"Someone's feet standing on a scale with a measuring tape in front of them.\" width=\"1023\" height=\"692\" \/> <img class=\"alignnone wp-image-1624\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010737\/Picture77-300x136.png\" alt=\"A graph of sample proportion p on the x axis against frequency on the y-axis. There is a peak at 0.2 on the x-axis with a frequency of approximately 225. The spaces between bars is approximately 0.05.\" width=\"1297\" height=\"588\" \/> <img class=\"alignnone wp-image-1625\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010742\/Picture78-300x134.png\" alt=\"A graph of sample proportion p on the x axis against frequency on the y-axis. There is a peak at approximately 0.6 on the x-axis with a frequency of approximately 112. The spaces between bars is approximately 0.02.\" width=\"1051\" height=\"466\" \/><img class=\"alignnone wp-image-1626\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010746\/Picture79-300x129.png\" alt=\"A graph of sample proportion p on the x axis against frequency on the y-axis. There is a peak at approximately 0.6 on the x-axis with a frequency of approximately 175. The spaces between bars is approximately 0.05.\" width=\"1021\" height=\"439\" \/> <img class=\"alignnone wp-image-1627\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010750\/Picture80-300x130.png\" alt=\"A graph of sample proportion p on the x axis against frequency on the y-axis. There is a peak at 0.2 on the x-axis with a frequency of approximately 150. The spaces between bars is approximately 0.02.\" width=\"1297\" height=\"562\" \/>\r\n<div style=\"text-align: left;\" align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Skill or Concept: I can . . .<\/td>\r\n<td>Questions to check your understanding<\/td>\r\n<td>Rating\r\nfrom 1 to 5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Describe how the center, spread, and shape of a sampling distribution of a sample proportion varies with the sample size, , and the population proportion, .<\/td>\r\n<td>1\u20134<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use a normal distribution to approximate probabilities involving a sample proportion.<\/td>\r\n<td>5, Parts A and B<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use a normal distribution to approximate percentiles of a sample proportion.<\/td>\r\n<td>5, Part C<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<dl>Glossary 9B<\/dl>\r\n<dl id=\"fs-id1170572229168\" class=\"definition\">\r\n \t<dt>sampling distribution<\/dt>\r\n \t<dd id=\"fs-id1170572229174\">the distribution showing how sample proportions vary from sample to sample.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572229190\" class=\"definition\">\r\n \t<dt>population distribution<\/dt>\r\n \t<dd id=\"fs-id1170572229195\">the distribution showing how individuals vary in a population.<\/dd>\r\n<\/dl>\r\nGlossary 9C\r\n<dl id=\"fs-id1170572482608\" class=\"definition\">\r\n \t<dt>percentile<\/dt>\r\n \t<dd id=\"fs-id1170572482614\">the value at which a certain percentage falls below that value.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482619\" class=\"definition\">\r\n \t<dt>Central Limit Theorem<\/dt>\r\n \t<dd id=\"fs-id1170572482624\">as the sample size gets larger, the distribution of the sample proportion will become closer to a normal distribution.<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>Sample<\/td>\n<td>Sample Proportion<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>Skill or Concept: I can . . .<\/td>\n<td>Questions to check your understanding<\/td>\n<td>Rating<br \/>\nfrom 1 to 5<\/td>\n<\/tr>\n<tr>\n<td>Identify whether a summary measure is a parameter or a statistic.<\/td>\n<td>1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Determine the appropriate type of plot for a given dataset.<\/td>\n<td>3, Part A<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simulate sample proportions of random samples of a given size from a population with known .<\/td>\n<td>4, 5<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Describe and interpret features of a sampling distribution of sample proportions.<\/td>\n<td>2<\/p>\n<p>3, Part B<\/p>\n<p>3, Part C<\/p>\n<p>4\u20136<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Calculate the standard deviation of a sample proportion.<\/td>\n<td>7<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1621\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010722\/Picture741-300x200.jpg\" alt=\"A display showing a graph labeled &quot;Unemployment.&quot;\" width=\"1097\" height=\"731\" \/>A dis<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1622\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010728\/Picture751-300x169.jpg\" alt=\"An illustration of various terms related to sampling and distribution. In the top left corner, there is a bubble labeled \u201cPopulation: U.S. Labor Force.\u201d Beneath this bubble is a bar chart titled \u201cPopulation Distribution.\u201d The bar chart is labeled \u201cEmployment Level\u201d on the x-axis and \u201cProportion\u201d on the y-axis. For \u201cEmployed,\u201d the count is approximately 0.85. For \u201cUnemployed,\u201d the count is approximately 0.15. Beneath this graph is a caption reading \u201cPopulation proportion that are unemployed: p = 0.15.\u201d From the bubble labeled \u201cPopulation: U.S. Labor Force,\u201d there are also several arrows pointing to other bubbles. Above them, there is text reading \u201cMany many random samples of size n = 50.\u201d The bubbles are labeled the following: \u201cp = 0.11,\u201d \u201cp = 0.12,\u201d \u201cp = 0.18,\u201d \u201cp = 0.16,\u201d \u201cp = 0.20,\u201d \u201cp = 0.22,\u201d \u201cp = 0.14,\u201d and \u201cp = 0.18.\u201d From the bubble labeled \u201cp = 0.12,\u201d there is a bar chart to the right titled \u201cSample Distribution.\u201d On the x-axis, it is labeled \u201cEmployment Level,\u201d and on the y-axis, it is labeled \u201cProportion.\u201d For \u201cEmployed,\u201d the proportion is approximately 0.88, while for \u201cUnemployed,\u201d the proportion is approximately 0.12. Each of the bubbles also has an arrow leading from it to a graph in the bottom righthand corner. This graph is titled \u201cSampling Distribution of Sample Proportion,\u201d with a subheading that reads \u201cMean = 0.15, Standard deviation = 0.0499 (10,000 simulations of samples of size n = 50).\u201d On the x-axis, the graph is labeled \u201cSample proportion p, and on the y-axis, the graph is labeled \u201cFrequency.\u201d The graph is a bar graph with a peak around approximately 0.14. There is a dot at approximately 0.15. Beneath this graph and the bubbles to its left, there is text that reads \u201cSample proportion that are unemployed: p (value varies from sample to sample).\u201d\" width=\"1022\" height=\"576\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1623\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010733\/Picture761-300x203.jpg\" alt=\"Someone's feet standing on a scale with a measuring tape in front of them.\" width=\"1023\" height=\"692\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1624\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010737\/Picture77-300x136.png\" alt=\"A graph of sample proportion p on the x axis against frequency on the y-axis. There is a peak at 0.2 on the x-axis with a frequency of approximately 225. The spaces between bars is approximately 0.05.\" width=\"1297\" height=\"588\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1625\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010742\/Picture78-300x134.png\" alt=\"A graph of sample proportion p on the x axis against frequency on the y-axis. There is a peak at approximately 0.6 on the x-axis with a frequency of approximately 112. The spaces between bars is approximately 0.02.\" width=\"1051\" height=\"466\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1626\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010746\/Picture79-300x129.png\" alt=\"A graph of sample proportion p on the x axis against frequency on the y-axis. There is a peak at approximately 0.6 on the x-axis with a frequency of approximately 175. The spaces between bars is approximately 0.05.\" width=\"1021\" height=\"439\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1627\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/19010750\/Picture80-300x130.png\" alt=\"A graph of sample proportion p on the x axis against frequency on the y-axis. There is a peak at 0.2 on the x-axis with a frequency of approximately 150. The spaces between bars is approximately 0.02.\" width=\"1297\" height=\"562\" \/><\/p>\n<div style=\"text-align: left; margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>Skill or Concept: I can . . .<\/td>\n<td>Questions to check your understanding<\/td>\n<td>Rating<br \/>\nfrom 1 to 5<\/td>\n<\/tr>\n<tr>\n<td>Describe how the center, spread, and shape of a sampling distribution of a sample proportion varies with the sample size, , and the population proportion, .<\/td>\n<td>1\u20134<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Use a normal distribution to approximate probabilities involving a sample proportion.<\/td>\n<td>5, Parts A and B<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Use a normal distribution to approximate percentiles of a sample proportion.<\/td>\n<td>5, Part C<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<dl> <\/dl>\n<dl id=\"fs-id1170572229168\" class=\"definition\">\n<dt>sampling distribution<\/dt>\n<dd id=\"fs-id1170572229174\">the distribution showing how sample proportions vary from sample to sample.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572229190\" class=\"definition\">\n<dt>population distribution<\/dt>\n<dd id=\"fs-id1170572229195\">the distribution showing how individuals vary in a population.<\/dd>\n<\/dl>\n<p>Glossary 9C<\/p>\n<dl id=\"fs-id1170572482608\" class=\"definition\">\n<dt>percentile<\/dt>\n<dd id=\"fs-id1170572482614\">the value at which a certain percentage falls below that value.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482619\" class=\"definition\">\n<dt>Central Limit Theorem<\/dt>\n<dd id=\"fs-id1170572482624\">as the sample size gets larger, the distribution of the sample proportion will become closer to a normal distribution.<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":23592,"menu_order":34,"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-1620","chapter","type-chapter","status-publish","hentry"],"part":704,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1620","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":5,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1620\/revisions"}],"predecessor-version":[{"id":2959,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1620\/revisions\/2959"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/704"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1620\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=1620"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=1620"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=1620"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=1620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}