{"id":"cb_question_bank:291ca418-ba54-48c5-8d87-ce47d383a200","source_id":"cb_question_bank","source_item_id":"291ca418-ba54-48c5-8d87-ce47d383a200","external_id":null,"ibn":"020263-DC","question_id":"f8f79e11","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":"A park ranger asked a random sample of visitors how far they hiked during their visit. Based on the responses, the estimated mean was found to be 4.5 miles, with an associated margin of error of 0.5 miles. Which of the following is the best conclusion from these data?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A park ranger asked a random sample of visitors how far they hiked during their visit. Based on the responses, the estimated mean was found to be 4.5 miles, with an associated margin of error of 0.5 miles. Which of the following is the best conclusion from these data?</p>\n","rationale_html":"<p>Choice D is correct. The given estimated mean has an associated margin of error because from sample data, the population mean can’t be determined precisely. Rather, from the sample mean, an interval can be determined within which it’s plausible that the population’s mean is likely to lie. Since the estimated mean is 4.5 miles with an associated margin of error of 0.5 miles, it follows that between <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6a7749edf8d4e8296ca127e023c8678fb291887b70ce4507c8b889750ba01548\" alt=\"4 point 5 minus 0 point 5 \"></span> miles and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9c6d548e7717abddefb6eb11ae5856847df38102c3ff561157a622ceee370875\" alt=\"4 point 5 plus 0 point 5\"></span> miles, or between 4 and 5 miles, is plausibly the mean distance hiked for all visitors.</p><p>Choices A, B, and C are incorrect. Based on the estimated mean, no determination can be made about the number of miles hiked for all visitors to the park.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.616000+00:00","source_updated_at":"2023-08-02T20:25:59.616000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">It is likely that all visitors hiked between 4 and 5 miles.</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">It is likely that most visitors hiked exactly 4.5 miles.</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">It is not possible that any visitor hiked less than 3 miles.</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.</p>\n","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}}