{"id":"cb_question_bank:db5c21a9-cf35-4099-bd40-7fd4a6e07386","source_id":"cb_question_bank","source_item_id":"db5c21a9-cf35-4099-bd40-7fd4a6e07386","external_id":"993a9eaf-5cb2-4e31-b138-e7b5002d37c5","ibn":null,"question_id":"1e562f24","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":"To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is 0.49 , with an associated margin of error of 0.04 . Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?","stimulus":"","stimulus_html":null,"stem_html":"<p>To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is <math alttext=\"0.49\"><mn>0.49</mn>\n</math>, with an associated margin of error of <math alttext=\"0.04\"><mn>0.04</mn>\n</math>. Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It’s given that the estimate for the proportion of the population that has the characteristic is <math alttext=\"0.49\"><mn>0.49</mn>\n</math> with an associated margin of error of <math alttext=\"0.04\"><mn>0.04</mn>\n</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 proportion of the population that has the characteristic. Therefore, it’s plausible that the proportion of the population that has this characteristic is between <math alttext=\"0.45\"><mn>0.45</mn>\n</math> and <math alttext=\"0.53\"><mn>0.53</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. A value less than <math alttext=\"0.45\"><mn>0.45</mn>\n</math> is outside the interval of plausible values for the proportion of the population that has the characteristic.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. The value <math alttext=\"0.49\"><mn>0.49</mn>\n</math> is an estimate for the proportion based on this sample. However, since the margin of error for this estimate is known, the most appropriate conclusion is not that the proportion is exactly one value but instead lies in an interval of plausible values.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. A value greater than <math alttext=\"0.53\"><mn>0.53</mn>\n</math> is outside the interval of plausible values for the proportion of the population that has the characteristic.</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>It is plausible that the proportion is between <math alttext=\"0.45\"><mn>0.45</mn>\n</math> and <math alttext=\"0.53\"><mn>0.53</mn>\n</math>.</p>","ord":0},{"label":"B","content_html":"<p>It is plausible that the proportion is less than <math alttext=\"0.45\"><mn>0.45</mn>\n</math>.</p>","ord":1},{"label":"C","content_html":"<p>The proportion is exactly <math alttext=\"0.49\"><mn>0.49</mn>\n</math>.</p>","ord":2},{"label":"D","content_html":"<p>It is plausible that the proportion is greater than <math alttext=\"0.53\"><mn>0.53</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}}