{"id":"cb_question_bank:6b336560-d7a0-4c38-94e9-dbc1e658a7a2","source_id":"cb_question_bank","source_item_id":"6b336560-d7a0-4c38-94e9-dbc1e658a7a2","external_id":"d0c73d6b-6fba-46e6-898b-9debc677ed82","ibn":null,"question_id":"f04d40b2","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":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"From a population of 50,000 people, 1,000 were chosen at random and surveyed about a proposed piece of legislation. Based on the survey, it is estimated that 35 percent sign of people in the population support the legislation, with an associated margin of error of 3 percent sign . Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?","stimulus":"","stimulus_html":null,"stem_html":"<p>From a population of <math alttext=\"50,000\"><mn>50,000</mn>\n</math> people, <math alttext=\"1,000\"><mn>1,000</mn>\n</math> were chosen at random and surveyed about a proposed piece of legislation. Based on the survey, it is estimated that <math alttext=\"35 percent sign\"><mn>35</mn>\n<mo>%</mo></math> of people in the population support the legislation, with an associated margin of error of <math alttext=\"3 percent sign\"><mn>3</mn>\n<mo>%</mo></math>. Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?</p>","rationale_html":"<p>Choice C is correct. It’s given that an estimated&nbsp;<math alttext=\"35 percent sign\"><mn>35</mn><mo>%</mo></math> of people in the population support the legislation, with an associated margin of error of <math alttext=\"3 percent sign\"><mn>3</mn><mo>%</mo></math>. Subtracting and adding the margin of error from the estimate gives an interval of plausible values for the true percentage of people in the population who support the legislation. Therefore, it’s plausible that between&nbsp;<math alttext=\"32 percent sign\"><mn>32</mn><mo>%</mo></math> and&nbsp;<math alttext=\"38 percent sign\"><mn>38</mn><mo>%</mo></math> of people in this population support the legislation. The corresponding numbers of people represented by these percentages in the population can be calculated by multiplying the total population, <math alttext=\"50,000\"><mn>50,000</mn>\n</math>, by <math alttext=\"0.32\"><mn>0.32</mn>\n</math> and by <math alttext=\"0.38\"><mn>0.38</mn>\n</math>, which gives <math alttext=\"50,000 left parenthesis 0.32 right parenthesis equals 16,000\"><mn>50,000</mn><mfenced><mn>0.32</mn></mfenced><mo>=</mo><mn>16,000</mn></math> and <math alttext=\"50,000 left parenthesis 0.38 right parenthesis equals 19,000\"><mn>50,000</mn><mfenced><mn>0.38</mn></mfenced><mo>=</mo><mn>19,000</mn></math>, respectively. It follows that any value in the interval <math alttext=\"16,000\"><mn>16,000</mn>\n</math> to <math alttext=\"19,000\"><mn>19,000</mn>\n</math> is a plausible value for the total number of people in the population who support the proposed legislation. Of the choices given, only <math alttext=\"16,750\"><mn>16,750</mn>\n</math> is in this interval.</p>\n<p>Choice A is incorrect. This is the number of people in the sample, rather than in the population, who support the legislation.</p>\n<p>Choice B is incorrect. This is the number of people in the sample who do not support the legislation.</p>\n<p>Choice D is incorrect. This is a plausible value for the total number of people in the population who do not support the proposed legislation.</p>","correct_answer":["C"],"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><math alttext=\"350\"><mn>350</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"650\"><mn>650</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"16,750\"><mn>16,750</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"31,750\"><mn>31,750</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}}