{"id":"cb_question_bank:3bf0ae78-5461-474e-85ff-5f25065119ab","source_id":"cb_question_bank","source_item_id":"3bf0ae78-5461-474e-85ff-5f25065119ab","external_id":"c69d7c49-d5b4-474f-92d3-d2ef20e9813a","ibn":null,"question_id":"e03f3477","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":"A sample consisting of 720 adults who own televisions was selected at random for a study. Based on the sample, it is estimated that 32 percent sign of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41 percent sign . Which of the following is the most plausible conclusion about all adults who own televisions?","stimulus":"","stimulus_html":null,"stem_html":"<p>A sample consisting of <math alttext=\"720\"><mn>720</mn>\n</math> adults who own televisions was selected at random for a study. Based on the sample, it is estimated that <math alttext=\"32 percent sign\"><mn>32</mn>\n<mo>%</mo></math> of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of <math alttext=\"3.41 percent sign\"><mn>3.41</mn>\n<mo>%</mo></math>. Which of the following is the most plausible conclusion about all adults who own televisions?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. It's given that based on a sample selected at random, it's estimated that <math alttext=\"32 percent sign\"><mn>32</mn><mo>%</mo></math> of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of&nbsp;<math alttext=\"3.41 percent sign\"><mn>3.41</mn><mo>%</mo></math>. Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true percentage of adults who own televisions who use their televisions to watch nature shows. This means it's plausible that between <math alttext=\"32 percent sign minus 3.41 percent sign\"><mn>32</mn><mo>%</mo><mo>-</mo><mn>3.41</mn><mo>%</mo></math>, or&nbsp;<math alttext=\"28.59 percent sign\"><mn>28.59</mn><mo>%</mo></math>, and&nbsp;<math alttext=\"32 percent sign plus 3.41 percent sign\"><mn>32</mn><mo>%</mo><mo>+</mo><mn>3.41</mn><mo>%</mo></math>, or&nbsp;<math alttext=\"35.41 percent sign\"><mn>35.41</mn><mo>%</mo></math>, of all adults who own televisions use their televisions to watch nature shows. Therefore, of the given choices, the most plausible conclusion is that between&nbsp;<math alttext=\"28.59 percent sign\"><mn>28.59</mn><mo>%</mo></math> and&nbsp;<math alttext=\"35.41 percent sign\"><mn>35.41</mn><mo>%</mo></math> of all adults who own televisions use their televisions to watch nature shows.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. To make a plausible conclusion about all adults who own televisions, the sample must be selected at random from all adults who own televisions, not just those who use their televisions to watch nature shows.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. Since the sample was selected at random from all adults who own televisions, a plausible conclusion can be made about all adults who own televisions.</p>","correct_answer":["B"],"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;\">More than <math alttext=\"35.41 percent sign\"><mn>35.41</mn>\n<mo>%</mo></math> of all adults who own televisions use their televisions to watch nature shows.</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">Between <math alttext=\"28.59 percent sign\"><mn>28.59</mn>\n<mo>%</mo></math> and <math alttext=\"35.41 percent sign\"><mn>35.41</mn>\n<mo>%</mo></math> of all adults who own televisions use their televisions to watch nature shows.&nbsp;</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">Since the sample included adults who own televisions and not just those who use their televisions to watch nature shows, no conclusion can be made.</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">Since the sample did not include all the people who watch nature shows, no conclusion can be made.</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}}