{"id":"cb_question_bank:ba5476dc-bbd8-4ec8-95dc-446960da8390","source_id":"cb_question_bank","source_item_id":"ba5476dc-bbd8-4ec8-95dc-446960da8390","external_id":"f2ee094c-7d77-427f-8375-dbbc8c6aa16b","ibn":null,"question_id":"4096a482","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.F.","skill":"Inference from sample statistics and margin of error","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Based on a random sample from a population, a researcher estimated that the mean value of a certain variable for the population is 20.5 , with an associated margin of error of 1 . Which of the following is the most appropriate conclusion?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Based on a random sample from a population, a researcher estimated that the mean value of a certain variable for the population is <math alttext=\"20.5\"><mn>20.5</mn>\n</math>, with an associated margin of error of <math alttext=\"1\"><mn>1</mn>\n</math>. Which of the following is the most appropriate conclusion?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that based on a random sample from a population, the estimated mean value for a certain variable for the population is <math alttext=\"20.5\"><mn>20.5</mn></math>, with an associated margin of error of <math alttext=\"1\"><mn>1</mn>\n</math>. This means that it is plausible that the actual mean value of the variable for the population is between&nbsp;<math alttext=\"20.5 minus 1\"><mn>20.5</mn><mo>-</mo><mn>1</mn></math> and&nbsp;<math alttext=\"20.5 plus 1\"><mn>20.5</mn><mo>+</mo><mn>1</mn></math>. Therefore, the most appropriate conclusion is that it is plausible that the actual mean value of the variable for the population is between <math alttext=\"19.5\"><mn>19.5</mn></math>&nbsp;and <math alttext=\"21.5\"><mn>21.5</mn></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. The estimated mean value and associated margin of error describe only plausible values, not all the possible values, for the actual mean value of the variable, so this is not an appropriate conclusion.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. The estimated mean value and associated margin of error describe only plausible values for the actual mean value of the variable, not all the possible values of the variable, so this is not an appropriate conclusion.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. Since <math alttext=\"20.5\"><mn>20.5</mn></math>&nbsp;is the estimated mean value of the variable based on a random sample, the actual mean value of the variable may not be exactly <math alttext=\"20.5\"><mn>20.5</mn></math>. Therefore, this is not an appropriate conclusion.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.835000+00:00","source_updated_at":"2023-08-02T20:25:59.835000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">It is plausible that the actual mean value of the variable for the population is between <math alttext=\"19.5\"><mn>19.5</mn>\n</math> and <math alttext=\"21.5\"><mn>21.5</mn>\n</math>.</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">It is not possible that the mean value of the variable for the population is less than <math alttext=\"19.5\"><mn>19.5</mn>\n</math> or greater than <math alttext=\"21.5\"><mn>21.5</mn>\n</math>.</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">Every value of the variable in the population is between <math alttext=\"19.5\"><mn>19.5</mn>\n</math> and <math alttext=\"21.5\"><mn>21.5</mn>\n</math>.</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">The mean value of the variable for the population is <math alttext=\"20.5\"><mn>20.5</mn>\n</math>.</p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}